Answers>Maths>A Level>Article

In a triangle ABC, side AB=10 cm, side AC=5cm and the angle BAC=θ, measured in degrees. The area of triangle ABC is 15cm(sq). Find 2 possible values for cosθ and the exact length of BC, given that it is the longest side of the triangle.

To find cosθ, use the formula for the area of a triangle i.e. AREA=1/2 x a x b x sinC.=> For this case: 15= 1/2 x 10 x 5 x sinC to find sinC.=> SinC = 3/5 thus, Arcsin(3/5)=+- 4/5 or +-0.8
To find the exact length of BC, use the cosine rule.=> c(sq)=a(sq)+b(sq)-2abCosC=> c(sq)=10(sq)+5(sq)-2(10)(5)(+-4/5)=> c(sq)= Square root of 205

Answered by • Maths tutor

24026 Views

See similar Maths A Level tutors

In a triangle ABC, side AB=10 cm, side AC=5cm and the angle BAC=θ, measured in degrees. The area of triangle ABC is 15cm(sq). Find 2 possible values for cosθ and the exact length of BC, given that it is the longest side of the triangle.

Related Maths A Level answers

In this question, take 'log' to mean 'log base 5'. Solve the equation log(x^2-5)-log(x) = 2*log(2)

Why is the derivative of a function its gradient?

(M1) What direction does friction act in? What are the friction equations both generally and in limiting equilibrium? What does it mean for a system to be in equilibrium?

Differentiate the function f(x) = 2x^3 + (cos(x))^2 + e^x