Solve a right triangle, and trigonometry word problems

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Ren looks down from a 45 m lighthouse tower at a boat. The angle of depression is 17°. How far is the boat from the base, to the nearest tenth?

   147.2
2. 2.

   Tala looks down from a 21 m cliff at a towel on the beach. The angle of depression is 26°. How far is the towel from the cliff's base, to the nearest tenth?

   43.1
3. 3.

   Ari looks down from the 15 m school roof at a bike at an angle of depression of 42°. How far is the bike from the building, to the nearest tenth?

   16.7
4. 4.

   Bo's eyes are 1.5 m above the ground, 20 m from a tree. The angle of elevation to the treetop is 38°. How tall is the tree, to the nearest tenth?

   17.1
5. 5.

   Esme's eyes are 1.6 m up, standing 35 m from a tower. The angle of elevation to the top is 26°. How tall is the tower, to the nearest tenth?

   18.7
6. 6.

   Jun's eyes are 1.2 m up, 15 m from a house. The angle of elevation to the chimney top is 51°. How high is the chimney top, to the nearest tenth?

   19.7
7. 7.

   Kira's eyes are 1.4 m up, 50 m from a castle tower at a fair. The angle of elevation to its top is 19°. How tall is it, to the nearest tenth?

   18.6
8. 8.

   Luz's sketch of a ramp is right triangle DFG: right angle at G, ∠D = 28°, DF = 16 ft. What are ∠F, FG and DG to the nearest tenth, in order with commas?

   62, 7.5, 14.1
9. 9.

   Noah's sketch of a kite string is right triangle DFG: right angle at G, ∠D = 57°, DF = 40 m. What are ∠F, FG and DG to the nearest tenth, in order with commas?

   33, 33.5, 21.8
10. 10.

    Pia's sketch of a tent rope is right triangle DFG: right angle at G, ∠D = 32°, DF = 9 ft. What are ∠F, FG and DG to the nearest tenth, in order with commas?

    58, 4.8, 7.6