Question

grade 11 chapter 1 test (college)
knowledge /12, thinking /12
communication /612 application /12

1. determine the value for each.

sin 30° = 0.5
tan 60° = 1.73
cos 50 = 0.64
sin a = 0.28 ∠a = 16.26°
tan a = 1 ∠a =
cos a = 0.6 ∠a =

1. in the diagram, determine each measure

a) ∠b = 50°
b) a=
c) b=

Explanation:

Step1: Find angle A when tan A = 1

Use inverse - tangent function. $\angle A=\arctan(1)$. Since $\tan45^{\circ}=1$, $\angle A = 45^{\circ}$.

Step2: Find angle A when cos A = 0.6

Use inverse - cosine function. $\angle A=\arccos(0.6)$. $\angle A\approx53.13^{\circ}$.

Step3: Find side a in right - triangle

Use sine function. $\sin B=\frac{b}{c}$, and $\sin50^{\circ}=\frac{a}{50}$, so $a = 50\sin50^{\circ}\approx50\times0.766 = 38.3$.

Step4: Find side b in right - triangle

Use cosine function. $\cos B=\frac{a}{c}$, and $\cos50^{\circ}=\frac{b}{50}$, so $b = 50\cos50^{\circ}\approx50\times0.643 = 32.15$.

Answer:

When $\tan A = 1$, $\angle A = 45^{\circ}$; when $\cos A = 0.6$, $\angle A\approx53.13^{\circ}$; $a\approx38.3$; $b\approx32.15$