Question

6. In right triangle ABC, mZC=3y-10,

m/B=y+ 40, and mZA= 90. What type of right
triangle is triangle ABC?
1) scalene
isosceles
3) equilateral
6 Dear
4) obtuse
32.5
y +40

Answer 1

scalene

Explanation:

step 1

Find the value of y

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

In this problem

m∠A+m∠B+m∠C=180°

substitute the given values

`90\°+(y+40)\°+(3y-10)\°=180\°`

Solve for y

`4y+120=180`

`4y=180-120`

`4y=60`

`y=15`

step 2

Find the measure of angle B

m∠B=(y+40)°

substitute the value of y

m∠B=(15+40)=55°

step 3

Find the measure of angle C

m∠C=(3y-10)°

substitute the value of y

m∠C=(3(15)-10)=35°

The three interior angles are different

so

The three sides of the ABC triangle will also be different

therefore

The right triangle ABC is scalene