Solve a right triangle, and trigonometry word problems

Answer Key - Grade 10 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Ren's ramp meets the ground at ∠D = 23°. The right angle is at G, under the top end F. What is ∠F?

   67
2. 2.

   Zee's kite string makes ∠D = 56° with the ground. The kite F is straight above G, a right angle. What is ∠F, between the string and the line down?

   34
3. 3.

   Ari's tent rope makes ∠D = 68° with the ground. The pole stands at G, a right angle. What is ∠F, between the rope and the pole?

   22
4. 4.

   Bo leans a 16 ft ladder on a wall at 72° to the ground. The sketch labels the ladder as the hypotenuse. How high up the wall does it reach, to the nearest tenth?

   15.2
5. 5.

   Esme's 12 ft ramp makes 13° with the ground. The sketch labels the ramp as the hypotenuse. How far along the ground does it run, to the nearest tenth?

   11.7
6. 6.

   A tree's shadow is 9 m long when the sun is 58° up. Kira's sketch labels the shadow as the adjacent leg. How tall is the tree, to the nearest tenth?

   14.4
7. 7.

   Luz's 14 ft ramp rises 3 ft. The sketch labels the rise as opposite ∠D and the ramp as the hypotenuse. What is ∠D, to the nearest tenth of a degree?

   12.4
8. 8.

   Milo's kite flies 31 m up on 50 m of string. The sketch labels the height as opposite ∠D and the string as the hypotenuse. What is ∠D, to the nearest tenth of a degree?

   38.3
9. 9.

   Noah's 13 ft ladder stands with its foot 4 ft from the wall. The sketch labels the foot distance as adjacent to ∠D. What is ∠D, to the nearest tenth of a degree?

   72.1
10. 10.

    A 15 m tree casts an 11 m shadow. Pia's sketch labels the height as opposite ∠D and the shadow as adjacent. What is ∠D, to the nearest tenth of a degree?

    53.7