5.4 Right triangle trigonometry  (Page 7/12)

A 23-ft ladder leans against a building so that the angle between the ground and the ladder is $\mathrm{80°}.$ How high does the ladder reach up the side of the building?

The angle of elevation to the top of a building in New York is found to be 9 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.

The angle of elevation to the top of a building in Seattle is found to be 2 degrees from the ground at a distance of 2 miles from the base of the building. Using this information, find the height of the building.

Assuming that a 370-foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be $\mathrm{60°},$ how far from the base of the tree am I?

$\frac{\pi }{4}$

$-\frac{5\pi }{3}$

-210°

180°

Find the length of an arc in a circle of radius 7 meters subtended by the central angle of 85°.

Find the area of the sector of a circle with diameter 32 feet and an angle of $\frac{3\pi }{5}$ radians.

$\mathrm{420°}$

$-\mathrm{80°}$

$-\frac{20\pi }{11}$

$\frac{14\pi }{5}$

-210°

75°

$\frac{5\pi }{4}$

$-\frac{\pi }{3}$

Find the linear speed of a point on the equator of the earth if the earth has a radius of 3,960 miles and the earth rotates on its axis every 24 hours. Express answer in miles per hour.

A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. What is the car's speed in miles per hour?

Find the exact value of $\sin \frac{\pi }{3}.$

Find the exact value of $\cos \frac{\pi }{4}.$

Find the exact value of $\cos \pi .$

State the reference angle for $\mathrm{300°}.$

State the reference angle for $\frac{3\pi }{4}.$

Compute cosine of $\mathrm{330°}.$

Compute sine of $\frac{5\pi }{4}.$

State the domain of the sine and cosine functions.

State the range of the sine and cosine functions.

$\cos \frac{\pi }{6}$

$\tan \frac{\pi }{4}$

$\csc \frac{\pi }{3}$

$\sec \frac{\pi }{4}$

$\sec \frac{11\pi }{3}$

$\sec \mathrm{315°}$

If $\sec \left(t\right)=-2.5$ , what is the $\text{sec}(-t)?$

If $\text{tan}(t)=-0.6,$ what is the $\text{tan}(-t)?$

If $\text{tan}(t)=\frac{1}{3},$ find $\text{tan}(t-\pi ).$

If $\text{cos}(t)=\frac{\sqrt{2}}{2},$ find $\text{sin}(t+2\pi ).$

Which trigonometric functions are even?

Which trigonometric functions are odd?

$\cos \frac{\pi }{4}$

$\cot \frac{\pi }{3}$

$\tan \frac{\pi }{6}$

$\cos \left(\frac{\pi }{2}\right)=\sin (\text{\_\_°})$

$\csc (18\text{°})=\sec (\text{\_\_°})$

$\cos B=\frac{3}{5},a=6$

$\tan A=\frac{5}{9},b=6$

$\sin A$

$\tan B$

A 15-ft ladder leans against a building so that the angle between the ground and the ladder is $\mathrm{70°}.$ How high does the ladder reach up the side of the building?

The angle of elevation to the top of a building in Baltimore is found to be 4 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building.

Convert $\frac{5\pi }{6}$ radians to degrees.

Convert $\mathrm{-620°}$ to radians.

Find the length of a circular arc with a radius 12 centimeters subtended by the central angle of $\mathrm{30°}.$

Find the area of the sector with radius of 8 feet and an angle of $\frac{5\pi }{4}$ radians.

Find the angle between $\mathrm{0°}$ and $\text{360°}$ that is coterminal with $\mathrm{375°}.$

Find the angle between 0 and $2\pi$ in radians that is coterminal with $-\frac{4\pi }{7}.$

Draw the angle $\mathrm{315°}$ in standard position on the Cartesian plane.

Draw the angle $-\frac{\pi }{6}$ in standard position on the Cartesian plane.

A carnival has a Ferris wheel with a diameter of 80 feet. The time for the Ferris wheel to make one revolution is 75 seconds. What is the linear speed in feet per second of a point on the Ferris wheel? What is the angular speed in radians per second?

Find the exact value of $\sin \frac{\pi }{6}.$

Compute sine of $\mathrm{240°}.$

State the domain of the sine and cosine functions.

State the range of the sine and cosine functions.

Find the exact value of $\cot \frac{\pi }{4}.$

Find the exact value of $\tan \frac{\pi }{3}.$

Use reference angles to evaluate $\csc \frac{7\pi }{4}.$

Use reference angles to evaluate $\tan 210°.$

If $\text{csc}t=0.68,$ what is the $\text{csc}(-t)?$

If $\text{cos}\text{t}=\frac{\sqrt{3}}{2},$ find $\text{cos}(t-2\pi ).$

Which trigonometric functions are even?

Find the missing angle: $\cos \left(\frac{\pi }{6}\right)=\sin \left(\_\_\_\right)$

Find the missing sides of the triangle $ABC:\sin B=\frac{3}{4},c=12$

Find the missing sides of the triangle.

The angle of elevation to the top of a building in Chicago is found to be 9 degrees from the ground at a distance of 2000 feet from the base of the building. Using this information, find the height of the building.