7.2 Right Triangle Trigonometry

Find the exact value of the trigonometric functions of $\frac{\pi}{3} ,$ using side lengths.

Find the exact value of the trigonometric functions of $\frac{\pi}{4} ,$ using side lengths.

If $\sin t = \frac{5}{12} ,$ find $\cos \left(\frac{\pi}{2} - t\right) .$

If $\csc \left(\frac{\pi}{6}\right) = 2 ,$ find $\text{sec} \left(\frac{\pi}{3}\right) .$

A right triangle has one angle of $\frac{\pi}{3}$ and a hypotenuse of 20. Find the unknown sides and angle of the triangle.

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 $\frac{5 \pi}{12}$ with the ground? Round to the nearest foot.

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

Explain the cofunction identity.

Use cofunctions of complementary angles.

$\cos \left(\frac{\pi}{3}\right) = \sin \left(___\right)$

Use cofunctions of complementary angles.

$\tan \left(\frac{\pi}{4}\right) = \cot \left(___\right)$

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.

$\sin B = \frac{1}{2} , a = 20$

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.

$\tan A = 100 , b = 100$

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.

$a = 5 , \measuredangle A = 60°$

$\sin A$

$\tan A$

$\text{sec} A$

$\sin A$

$\tan A$

$\text{sec} A$

Use a calculator to find the length of each side to four decimal places.

$b = 15 , \measuredangle B = 15°$

Use a calculator to find the length of each side to four decimal places.

$c = 50 , \measuredangle B = 21°$

Use a calculator to find the length of each side to four decimal places.

$b = 3.5 , \measuredangle A = 78°$

A radio tower is located 325 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is $43° ,$ and that the angle of depression to the bottom of the tower is $31° .$ How tall is the tower?

A 400-foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is $18° ,$ and that the angle of depression to the bottom of the monument is $3° .$ How far is the person from the monument?

There is lightning rod on the top of a building. From a location 500 feet from the base of the building, the angle of elevation to the top of the building is measured to be $36° .$ From the same location, the angle of elevation to the top of the lightning rod is measured to be $38° .$ Find the height of the lightning rod.

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