Lesson 117: Using Trigonometric Ratios — Practice Questions

1. 1. In a right triangle, an angle measures $55^{\circ}$. The side adjacent to this angle is $x$ and the hypotenuse is 20. Find the value of $x$, rounded to the nearest hundredth. $x$ = ___

2. 2. From a point 50 feet away from the base of a flagpole, the angle of elevation to the top is $40^{\circ}$. What is the height of the flagpole to the nearest tenth of a foot?

   • A. 32.1 ft
   • B. 38.3 ft
   • C. 42.0 ft
   • D. 59.6 ft

3. 3. In a right triangle, one angle is $28^{\circ}$. The side opposite this angle is 10 units long. What is the length of the hypotenuse, rounded to the nearest tenth? ___

4. 4. In a right triangle, the side adjacent to angle B is 5 and the hypotenuse is 13. What is the value of $ \operatorname{sec} B $?

   • A. $ \frac{5}{13} $
   • B. $ \frac{13}{5} $
   • C. $ \frac{12}{5} $
   • D. $ \frac{5}{12} $

5. 5. If the value of $ \operatorname{cos} \theta = \frac{11}{61} $, what is the exact value of $ \operatorname{sec} \theta $? ___

6. 6. To find a building's height, you measure the angle of elevation from the ground and your distance to its base. Which trig ratio connects the height, your distance, and the angle?

   • A. Sine
   • B. Cosine
   • C. Tangent
   • D. Hypotenuse

7. 7. In a right triangle, the leg opposite a $35^{\circ}$ angle is unknown. If the hypotenuse is 10, what is the length of the opposite leg, $x$? Round to two decimal places. $x$ = ___

8. 8. A support wire is attached to the top of a pole. The wire makes a $75^{\circ}$ angle with the ground at a point 8 feet from the pole's base. Find the length of the wire, rounded to the nearest hundredth. ___ feet

9. 9. You stand 40 feet from a tree and measure a $50^{\circ}$ angle of elevation to its top. Which equation correctly finds the tree's height, $h$?

   • A. $ h = 40 \cdot \tan(50^{\circ}) $
   • B. $ h = \frac{40}{\tan(50^{\circ})} $
   • C. $ h = 40 \cdot \sin(50^{\circ}) $
   • D. $ h = 40 \cdot \cos(50^{\circ}) $

10. 10. Simplify the expression $(12m^5 n^8)^0$, assuming $m$ and $n$ are not zero. The result is ___.