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
Related Maths A Level answers
All answers ▸The equation " x^3-3x+1=0 " has three real roots. Show that one of the roots lies between −2 and −1
Solve the following equation: 4(sinx)^2+8cosx-7=0 in the interval 0=<x=<360 degrees.
Given that 2log2(x+15) -log2(x) = 6, show that x^2-34x+225=0
How do you intergrate ln(x)?