Question

1. tan x

z
15
17
y
8
x

1. sin x

z
35
y
37
12
x

1. sin a

b
10
8
a
6
c

Explanation:

Problem 10: $\boldsymbol{\tan X}$

Step1: Recall tangent definition

In a right triangle, $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$ to $\theta$. For $\angle X$, opposite side is $YZ = 15$, adjacent side is $YX = 8$.

Step2: Calculate $\tan X$

$\tan X = \frac{YZ}{YX} = \frac{15}{8}$

Step1: Recall sine definition

$\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$ to $\theta$. For $\angle X$, opposite side is $ZY = 35$, hypotenuse is $ZX = 37$.

Step2: Calculate $\sin X$

$\sin X = \frac{ZY}{ZX} = \frac{35}{37}$

Step1: Recall sine definition

$\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$ to $\theta$. For $\angle A$, opposite side is $BC = 8$, hypotenuse is $AB = 10$.

Step2: Calculate $\sin A$

$\sin A = \frac{BC}{AB} = \frac{8}{10} = \frac{4}{5}$

Answer:

$\boldsymbol{\frac{15}{8}}$

Problem 11: $\boldsymbol{\sin X}$