To find the height of a tree, a person walks to a point 30 feet from the base of the tree. She measures an angle of
between a line of sight to the top of the tree and the ground, as shown in
[link] . Find the height of the tree.
We know that the angle of elevation is
and the adjacent side is 30 ft long. The opposite side is the unknown height.
The trigonometric function relating the side opposite to an angle and the side adjacent to the angle is the tangent. So we will state our information in terms of the tangent of
letting
be the unknown height.
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
with the ground? Round to the nearest foot.
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Key equations
Cofunction Identities
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 permits 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 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?
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
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
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.
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
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?
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
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?
