In the diagram below, is an isosceles triangle with PQ =PR. QPR = 54° and QR= 20cm calculate to 2s.f
A PQR
B. The side PQ
C The Altitude of the triangle
D. The sum of PQR
Since PQ = PR, triangle PQR is an isosceles triangle. Therefore, angle PRQ is also equal to 54°.
To find angle QRP, we can use the fact that the sum of the interior angles of a triangle is 180°.
So, angle QRP = 180° - 54° - 54° = 72°.
Since PQ = PR = QR = 20cm, all sides of the triangle are equal in length.
Now, we can use the cosine rule to find side PQ:
PQ² = PR² + QR² - 2*PR*QR*cos(54°)
PQ² = 20² + 20² - 2*20*20*cos(54°)
PQ² = 400 + 400 - 800*cos(54°)
PQ² = 800 - 800*cos(54°)
PQ ≈ √(800 - 800*cos(54°)) ≈ √322 ≈ 17.96 cm
To find the altitude of the triangle, we can use the sine rule:
Altitude = PR*sin(54°) ≈ 20*sin(54°) ≈ 16.11 cm
Therefore:
A. PQR is an isosceles triangle.
B. The side PQ is approximately 17.96 cm.
C. The Altitude of the triangle is approximately 16.11 cm.
D. The sum of PQR is 54° + 72° + 54° = 180°.