<< Chapter < Page Chapter >> Page >

How long a ladder is needed to reach a windowsill 50 feet above the ground if the ladder rests against the building making an angle of 5 π 12 with the ground? Round to the nearest foot.

About 52 ft

Got questions? Get instant answers now!

Key equations

Trigonometric Functions Sine sin  t = opposite hypotenuse Cosine cos  t = adjacent hypotenuse Tangent tan  t = opposite adjacent Secant sec  t = hypotenuse adjacent Cosecant csc  t = hypotenuse opposite Cotangent cot  t = adjacent opposite
Reciprocal Trigonometric Functions sin  t = 1 csc  t csc  t = 1 sin  t cos  t = 1 sec  t sec  t = 1 cos  t tan  t = 1 cot  t cot  t = 1 tan  t
Cofunction Identities cos  t = sin ( π 2 t ) sin  t = cos ( π 2 t ) tan  t = cot ( π 2 t ) cot  t = tan ( π 2 t ) sec  t = csc ( π 2 t )

Key concepts

  • We can define trigonometric functions as ratios of the side lengths of a right triangle. See [link] .
  • The same side lengths can be used to evaluate the trigonometric functions of either acute angle in a right triangle. See [link] .
  • We can evaluate the trigonometric functions of special angles, knowing the side lengths of the triangles in which they occur. See [link] .
  • Any two complementary angles could be the two acute angles of a right triangle.
  • If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa. See [link] .
  • We can use trigonometric functions of an angle to find unknown side lengths.
  • Select the trigonometric function representing the ratio of the unknown side to the known side. See [link] .
  • Right-triangle trigonometry facilitates the measurement of inaccessible heights and distances.
  • The unknown height or distance can be found by creating a right triangle in which the unknown height or distance is one of the sides, and another side and angle are known. See [link] .

Section exercises

Verbal

For the given right triangle, label the adjacent side, opposite side, and hypotenuse for the indicated angle.


A right triangle.


A right triangle with side opposite, adjacent, and hypotenuse labeled.

Got questions? Get instant answers now!

When a right triangle with a hypotenuse of 1 is placed in a circle of radius 1, which sides of the triangle correspond to the x - and y -coordinates?

Got questions? Get instant answers now!

The tangent of an angle compares which sides of the right triangle?

The tangent of an angle is the ratio of the opposite side to the adjacent side.

Got questions? Get instant answers now!

What is the relationship between the two acute angles in a right triangle?

Got questions? Get instant answers now!

Explain the cofunction identity.

For example, the sine of an angle is equal to the cosine of its complement; the cosine of an angle is equal to the sine of its complement.

Got questions? Get instant answers now!

Algebraic

For the following exercises, use cofunctions of complementary angles.

cos ( 34° ) = sin ( ___° )

Got questions? Get instant answers now!

cos ( π 3 ) = sin ( ___ )

π 6

Got questions? Get instant answers now!

csc ( 21° ) = sec ( ___° )

Got questions? Get instant answers now!

tan ( π 4 ) = cot ( ___ )

π 4

Got questions? Get instant answers now!

For the following exercises, find the lengths of the missing sides if side a is opposite angle A , side b is opposite angle B , and side c is the hypotenuse.

cos B = 4 5 , a = 10

Got questions? Get instant answers now!

sin B = 1 2 , a = 20

b = 20 3 3 , c = 40 3 3

Got questions? Get instant answers now!

tan A = 5 12 , b = 6

Got questions? Get instant answers now!

tan A = 100 , b = 100

a = 10,000 , c = 10,00.5

Got questions? Get instant answers now!

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 6

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask