PQR is an isosceles triangle in which PQ=PR=6cm and QR =8cm. What is the value of the tangent of angleܴܳܲ ?

Answer:

8) E

Divide the isosceles triangle into two right-angled triangles by joining the midpoint of the largest side with the top vertex. Label the midpoint of QR as M.

QM = 8 ÷ 2 = 4 (since M is the midpoint of QR)

We first need to find the value of PM.
Using Pythagoras,

PQ² = QM² + PM²
6² = 4² + PM²
36 – 16 = PM²
PM² = 20
PM = √20 = √(2 x 2 x 5) = 2√5

tanθ = Opposite ÷ Adjacent = PM ÷ QM

tanθ = 2√5 = √5
4 2