Question

1. determine the measure of each angle, to the nearest degree. a) tan a = 0.7 b) tan θ = 1.75 c) tan β = 0.5543 d) tan c = 1.1504 illustrate each tangent ratio.

Explanation:

Part (a): $\tan A = 0.7$

Step 1: Recall the inverse tangent function

To find the angle \( A \) when we know the tangent of the angle, we use the inverse tangent function (also called arctangent), denoted as \( \tan^{-1} \) or \( \arctan \). So we need to calculate \( A=\tan^{-1}(0.7) \).

Step 2: Use a calculator to find the angle

Using a calculator (make sure it is in degree mode), we calculate \( \tan^{-1}(0.7) \).
\( A=\tan^{-1}(0.7)\approx35^\circ \) (rounded to the nearest degree)

Part (b): $\tan \theta = 1.75$

Step 1: Recall the inverse tangent function

To find the angle \( \theta \) when we know the tangent of the angle, we use the inverse tangent function \( \tan^{-1} \). So we need to calculate \( \theta=\tan^{-1}(1.75) \).

Step 2: Use a calculator to find the angle

Using a calculator (in degree mode), we calculate \( \tan^{-1}(1.75) \).
\( \theta=\tan^{-1}(1.75)\approx60^\circ \) (rounded to the nearest degree)

Part (c): $\tan \beta = 0.5543$

Step 1: Recall the inverse tangent function

To find the angle \( \beta \) when we know the tangent of the angle, we use the inverse tangent function \( \tan^{-1} \). So we need to calculate \( \beta=\tan^{-1}(0.5543) \).

Step 2: Use a calculator to find the angle

Using a calculator (in degree mode), we calculate \( \tan^{-1}(0.5543) \).
\( \beta=\tan^{-1}(0.5543)\approx29^\circ \) (rounded to the nearest degree)

Part (d): $\tan C = 1.1504$

Answer:

s:
a) \( \boldsymbol{35^\circ} \)
b) \( \boldsymbol{60^\circ} \)
c) \( \boldsymbol{29^\circ} \)
d) \( \boldsymbol{49^\circ} \)