Question

State if each triangle is acute, obtuse, or right.3)4 mi3 mi√√8 miA) RightC) ObtuseB) Acute

Answer 1

STEP - BY - STEP EXPLANATION

What to do?

Determine if the triangle is acute, right or obtuse.

Given:

Let side a= √8

side b= 3

side c= 4

Let the angle opposite side c= angle C

Step 1

Solve for angle c using the cosine formula.

`c^2=a^2+b^2-2ab\text{ }cosC`
`4^2=(√(8))^2+3^2-2(√(8))(3)cosC`
`6√(8)\text{ }cosC=8+9-16`
`\begin{gathered} cosC=(1)/(6√(8)) \\ \\ cosC=0.05893 \end{gathered}`
`C=cos^(-1)(0.05893)`
`C=86.62`

Step 2

Identify the measure of each given type of triangle.

Right - triangle is a triangle with angle 90 degree.

Acute triangle is a triangle with all angles less than 90 degree.

Obtuse triangle is a triangle with an angle more than 90 degree.

Step 3

Draw conclusion from the above definition.

Since the largest angle in the triangle is 86.62 degrees which is less than 90 degree, then it is an acute triangle.

ANSWER

B. Acute triangle.