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

Answer:

x ≈ 49.7°

Step-by-step 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]

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

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

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

cos(x) = $\frac{11}{17}$

x = 49.68°

x ≈ 49.7°