Question

use this diagram of triangle XYZ to answer the questions.
1)what is the value of side XY?5,10,50,100
2)what is the value of sin(x)?3/4,4/3,4/5,5/4
3)what is the value of cos(x)?4/5,5/4,3/5,5/3
4)what is the value of tan(x)?3/4,4/3,4/5,3/5

Answer 1

The sides of a triangle may or may not be congruent.

• The value of side XY is 10
• The value of sin(x) is 4/5
• The value of cos(x) is 3/5
• The value of tan(x) is 4/3

(a) Side XY

This is calculated using the following Pythagoras theorem.

$\mathbf{XY^2 = YZ^2 + XZ^2}$

$\mathbf{XY^2 = 8^2 + 6^2}$

$\mathbf{XY^2 = 64 + 36}$

$\mathbf{XY^2 = 100}$

Take positive square roots of both sides

$\mathbf{XY = 10}$

Hence, the value of side XY is 10

(b) sin(x)

This is calculated using the following sine ratio

$\mathbf{sin(x) = \frac{YZ}{XY}}$

So, we have:

$\mathbf{sin(x) = \frac{8}{10}}$

Simplify

$\mathbf{sin(x) = \frac{4}{5}}$

Hence, the value of sin(x) is 4/5

(c) sin(x)

This is calculated using the following cosine ratio

$\mathbf{cos(x) = \frac{XZ}{XY}}$

So, we have:

$\mathbf{cos(x) = \frac{6}{10}}$

Simplify

$\mathbf{cos(x) = \frac{3}{5}}$

Hence, the value of cos(x) is 3/5

(d) sin(x)

This is calculated using the following tangent ratio

$\mathbf{tan(x) = \frac{YZ}{XZ}}$

So, we have:

$\mathbf{tan(x) = \frac{8}{6}}$

Simplify

$\mathbf{tan(x) = \frac{4}{3}}$

Hence, the value of tan(x) is 4/3

Read more about right triangles at:

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