Question

a right - angled triangle and three equations are shown below.
a) which equation is correct: a, b or c?
a sin θ = 3/7
b cos θ = 3/7
c tan θ = 3/7
b) work out the size of angle θ.
give your answer to 1 d.p.
not drawn accurately

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - angled triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For angle $\theta$, the opposite side has length $3$ cm and the adjacent side has length $7$ cm.

Step2: Identify the correct trigonometric equation

Since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, and the opposite side to $\theta$ is $3$ cm and the adjacent side is $7$ cm, the correct equation is $\tan\theta = \frac{3}{7}$. So the answer to part (a) is C.

Step3: Calculate the angle $\theta$

We know that $\theta=\arctan(\frac{3}{7})$. Using a calculator, $\theta=\arctan(\frac{3}{7})\approx23.2^{\circ}$ (to 1 decimal place).

Answer:

a) C. $\tan\theta=\frac{3}{7}$
b) $23.2^{\circ}$