The value of PR is 13.04 units
Area of a triangle
The area of a triangle with sides a, b and angle Ф between them is given as A = 1/2absinФ.
Area of △PQR
Since △PQR is an inscribed triangle, the area of △PQR, A = 1/2PQPRsinP, where A = 50 and P = 36°
Also in △PQR, tanP = PQ/PR
So, making PQ subject of the formula, we have
PQ = PRtanP
Substituting the value of PQ into A, we have
A = 1/2PQPRsinP
A = 1/2(PRtanP)PRsinP
A = 1/2PR²tanPsinP
The value of PR
Making PR subject of the formula, we have
PR = √(2A/tanPsinP)
Given that A = 50 and P = 36°,substituting the values of the variables into the equation, we have
PR = √(2A/tanPsinP)
PR = √(2 × 50/tan36°sin36°)
PR = √[100/(0.7265 × 0.8090)]
PR = √[100/0.5878)
PR = √170.13
PR = 13.04
So, the value of PR is 13.04 units
Learn more about inscribed triangles here:
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