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\tyour solution\tcorrect solution
(a) sin 65°
(b) tan 60°
(c) cos 60°
calculate the following unknown angle measures. round your answer to the nearest degree.
question\tyour solution\tcorrect solution
(a) cos a = 0.6789
= 0.4455
(c) sin b = 0.1234

Explanation:

Part 1: Primary Trigonometric Ratio Calculations

(a) $\sin65^{\circ}$

Using a scientific calculator, we input $\sin(65)$
$$\sin65^{\circ}\approx0.9063$$

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

Using a scientific calculator, we input $\tan(60)$
$$\tan60^{\circ}\approx1.7321$$

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

Using a scientific calculator, we input $\cos(60)$
$$\cos60^{\circ}=0.5$$

Part 2: Calculate the unknown angle measures

(a) $\cos A = 0.6789$

We use the inverse cosine function, $A=\cos^{-1}(0.6789)$
Using a scientific calculator, $A\approx47^{\circ}$

(b) $\sin B=0.4455$

We use the inverse sine function, $B = \sin^{-1}(0.4455)$
Using a scientific calculator, $B\approx26^{\circ}$

(c) $\sin B=0.1234$

We use the inverse sine function, $B=\sin^{-1}(0.1234)$
Using a scientific calculator, $B\approx7^{\circ}$

Answer:

Question	Your Solution	Correct Solution
(b) $\tan60^{\circ}$	$\approx1.7321$	$1.7321$
(c) $\cos60^{\circ}$	$0.5$	$0.5$
(a) $\cos A = 0.6789$	$\approx47^{\circ}$	$47^{\circ}$
(b) $\sin B = 0.4455$	$\approx26^{\circ}$	$26^{\circ}$
(c) $\sin B=0.1234$	$\approx7^{\circ}$	$7^{\circ}$