Question

determining side lengths of special right triangles what are the lengths of the other two sides of the triangle? a 60° 10 30° c b ac = 5 and bc = 5 ac = 5 and bc = 5√5 ac = 5√3 and bc = 5 ac = 5 and bc = 5√3

Explanation:

Step1: Identify triangle type

This is a 30-60-90 right triangle, hypotenuse $AB=10$.

Step2: Find short leg (BC)

Short leg = $\frac{1}{2}\times$ hypotenuse
$BC = \frac{1}{2} \times 10 = 5$

Step3: Find long leg (AC)

Long leg = short leg $\times \sqrt{3}$
$AC = 5 \times \sqrt{3} = 5\sqrt{3}$

Answer:

AC = $5\sqrt{3}$ and BC = 5