Question

An isosceles triangle has angle measures 40°, 40°, and 100° the side across from the 100° angle is 10 inches long how long are the other sides

a. 6.43 in
b. 6.53 in
c. 15.32 in
d. 10 in

Answer 1

B is the correct answer, u can use the sine rule

Answer 2

B = C = 6.53 in

Explanation:

Given:-

- The three angles of an isosceles triangle are given as:

∠ A = 100° , ∠ B = 40° , ∠ C = 40°

- Side Length opposite to ∠ A, A = 10 in

Find:-

long how long are the other sides

Solution:-

- We can apply the sine rule to determine the similar side lengths of an isosceles triangle. The sine rules correlates the ratios of all the "sin ( Angle )" to their opposite side lengths to be equal.

A / sin (∠ A) = B / sin (∠ B) = C / sin ( ∠ C )

- So using the data we can compute side lengths B and C as follows:

B = C = A * sin ( ∠ B ) / sin (∠ A)

B = C = 10* [ sin ( 40 ) / sin ( 100 ) ]

B = C = 6.53 in