Question

The vertex angle of an isosceles triangle measures 26° . The base is 30 units long. What is the length of a leg of the isosceles triangle to the nearest tenth?

Answer 1

65.46 units

Explanation:

Given the information:

• The vertex angle of an isosceles triangle measures 26°

=> the leg angle is:

= (180° - 26° )/2

= 77°

• The base is 30 units

Let x is the length of the leg side (x>0)

We use cosine law to find x, we have:

`30^(2)` =
`x^(2) +x^(2) -2xxCos(26)` Because the isosceles has two equal leg sides

<=>
`30^(2)` = 2
`x^(2)` - 1.79
`x^(2)`

<=> 0.21
`x^(2)` =
`30^(2)`

<=>
`x^(2) =4285`

<=> x = 65.46 units

Hope it will find you well.