Question

Please help me!! High School algebra 2 math. Big Ideas Math

Answer 1

Answer:

x = 8

Step-by-step explanation:

Hello!

The missing angle in the triangle can be found by subtracting 90° and 45° from 180°. The missing angle is 45°.

This means that the triangle is isosceles, as there are two congruent base angles, 45° and 45°.

The side lengths opposite these two angles are congruent.

We can see that 8 is opposite 45°, and x is opposite 45°. Therefore, x must be equal to 8.

The value of x is 8.

Answer 2

Answer:

x = 8

Step-by-step explanation:

The interior angles of a triangle sum to 180°.

The given triangle is a right triangle, so the missing angle is 45°

⇒ 180° - 90° - 45° = 45°

As the triangle has 2 equal angles, this means it is an isosceles triangle (with its vertex at the right angle).  An isosceles triangle has legs of equal measure, therefore $x=8$.

Proof

This can be proven by using the tan trigonometric ratio to calculate the value of x.

Tan trig ratio

$\sf tan(\theta)=\dfrac{O}{A}$

where:

• $\theta$ is the angle
• O is the side opposite the angle
• A is the side adjacent the angle

Given:

• $\theta$ = 45°
• O = 8
• A = x

Substituting the given values into the equation and solving for x:

$\implies \tan (45^{\circ})=\dfrac{8}{x}$

$\implies x=\dfrac{8}{\tan (45^{\circ})}$

$\implies x=\dfrac{8}{1}$

$\implies x=8$