Search 75,514 tutors
FIND TUTORS
Ask a question
0 0

Suppose you have an isosceles triangle

Suppose you have an isosceles triangle, and each of the equal sides has a length of foot. Suppose the angle formed by those two sides is 45 degrees . The area of the triangle is 0.3536 square feet.
Suppose you have an isosceles triangle, and each of the equal sides has a length of r feet. Suppose the angle formed by those two sides is t .
 
what is the area of the triangle in square feet? 
Tutors, please sign in to answer this question.

2 Answers

Area of the triangle, A = (1/2)base x height = (1/2) 2rsin(t/2) rcos(t/2)
Answer: A = (1/2)r2sint
 
Check: r = 1, t = 45, A = (1/2)sin(45) = .3536
---------
Attn: You can extend it to two unequal sides a and b, and the angle t included by the two sides.
A = (1/2)absint
Area of a triangle is 1/2*base*altitude. For a triangle with sides a and b and angle θ between them, altitude to side a is b*sinθ. Therefore, area of a triangle is:
 
S=½a*b*sin(θ).
 For isosceles triangle:
 
S=½a2*sin(θ). If the side is 1 foot and θ=45°, then S=0.5*12*sin(45)=(√2)/4≈0.3536 ft2
 
For the isosceles triangle with the side r and angle t, area is given by:
 
S=½r2*sin(t)