Question

what is the measure of the base angle,x, of the isosceles triangle shown below? round your answer to the nearest tenth of a degree.​

Answer 1

x ≈ 49.7°

Explanation:

Since, the given triangle is an isosceles triangle,

Two sides having measure 17 units are equal.

Opposite angles of these equal sides will be equal.

Measure of the third angle = 180° - (x + x)°

By sine rule,

`\frac{\text{sinx}}{17}=\frac{\text{sin}(180-2x)}{22}`

`\frac{\text{sinx}}{17}=\frac{\text{sin}(2x)}{22}` [Since, sin(180 - θ) = sinθ]

`\frac{\text{sinx}}{17}=\frac{2(\text{sin}x)(\text{cos}x)}{22}`

`\frac{\text{sinx}}{17}=\frac{(\text{sin}x)(\text{cos}x)}{11}`

`(1)/(17)=\frac{(\text{cos}x)}{11}`

cos(x) =
`(11)/(17)`

x = 49.68°

x ≈ 49.7°