Question

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

Answer 1

x = 8

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

x = 8

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)=(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))=(8)/(x)`

`\implies x=(8)/(\tan (45^(\circ)))`

`\implies x=(8)/(1)`

`\implies x=8`