📐 Trigonometry in Right Triangles: SOH-CAH-TOA

Questions in this quiz

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1. Question 1

   In a right triangle, the side opposite angle $\theta$ is 5 cm and the hypotenuse is 13 cm. Which trigonometric ratio would you use first to find $\theta$?

2. Question 2

   In a right triangle, if one acute angle is 35°, the other acute angle must be 55°.

3. Question 3

   To find an unknown angle using trigonometry, you use the ___ function (such as $\sin^{-1}$, $\cos^{-1}$, or $\tan^{-1}$).

4. Question 4

   In right triangle $ABC$ with the right angle at $C$, $AB = 15$ cm (hypotenuse) and $AC = 9$ cm. What is the length of $BC$ to 1 decimal place?

5. Question 5

   For any acute angle $\theta$ in a right triangle, $\sin^2(\theta) + \cos^2(\theta) = 1$.

6. Question 6

   A ladder leans against a wall. The angle of elevation from the ground to the top of the ladder is 62°, and the ladder is 8 metres long. The height up the wall is approximately ___ metres.

7. Question 7

   In right triangle $PQR$ with right angle at $Q$, $\tan(P) = \frac{7}{5}$. Which statement is correct?

8. Question 8

   If $\cos(\theta) = 0.6$ for an acute angle $\theta$, then $\sin(\theta) = 0.8$.

9. Question 9

   A surveyor measures the angle of elevation to the top of a building from a point 50 m away as 35°. The building is approximately ___ m tall.

10. Question 10

    Arrange these steps in the correct order to solve a right triangle problem when given an angle and one side.