Question

using primary trig ratios to solve for angles & side lengths
part 1: primary trigonometric ratio calculations
calculate the following ratios. round your answers to 4 decimal places
question
your solution
correct solution
(a) sin 55°
sin 55 = 0.8

(b) tan 60°

(c) cos 60°

calculate the following unknown angle measures. round your answer to the nearest degree
question
your solution
correct solution
(a) cos a = 0.6789

(b) tan θ = 0.4455

(c) sin b = 0.1234

Explanation:

Part 1: Primary Trigonometric Ratio Calculations

(a) $\sin55^{\circ}$

Use a scientific calculator in degree - mode.
$$\sin55^{\circ}\approx0.8192$$

(b) $\tan60^{\circ}$

We know that $\tan60^{\circ}=\sqrt{3}$.
$$\tan60^{\circ}\approx1.7321$$

(c) $\cos60^{\circ}$

We know that $\cos60^{\circ}=\frac{1}{2}$.
$$\cos60^{\circ}=0.5000$$

Part 2: Calculating Unknown Angle Measures

(a) $\cos A = 0.6789$

Use the inverse cosine function $A=\cos^{-1}(0.6789)$.
$$A=\cos^{-1}(0.6789)\approx47^{\circ}$$

(b) $\tan\theta=0.4455$

Use the inverse tangent function $\theta = \tan^{-1}(0.4455)$.
$$\theta=\tan^{-1}(0.4455)\approx24^{\circ}$$

(c) $\sin B=0.1234$

Use the inverse sine function $B=\sin^{-1}(0.1234)$.
$$B=\sin^{-1}(0.1234)\approx7^{\circ}$$

Answer:

Question	Your Solution	Correct Solution
(b) $\tan60^{\circ}$		$1.7321$
(c) $\cos60^{\circ}$		$0.5000$
(a) $\cos A = 0.6789$		$47^{\circ}$
(b) $\tan\theta=0.4455$		$24^{\circ}$
(c) $\sin B=0.1234$		$7^{\circ}$