SOLUTION: Please help me pick the correct answer. 2 sides of an isosceles triangle each measure 10 inches and the vertex angle measures 40 degrees. Find the length of the altitude to the

Click here to see ALL problems on Triangles

Question 121466: Please help me pick the correct answer.
2 sides of an isosceles triangle each measure 10 inches and the vertex angle measures 40 degrees. Find the length of the altitude to the base to the nearest tenth of an inch.
Answers:
a) 9.4 inches
b) 9.9 inches
c) 10.2 inches
d) 10.8 inches
e) 11.3 inches
Answer by algebrapro18(249) (Show Source):
You can put this solution on YOUR website!
2 sides of an isosceles triangle each measure 10 inches and the vertex angle measures 40 degrees. Find the length of the altitude to the base to the nearest tenth of an inch.

Well using this we can construct the triangle and then use trig relations to solve for that length.

We know that the angle measure is 1/2(40) degrees because the altitude will bisect the vertex angel. We also know that when an altitude is drawn from the top of the triangle to the base that it bisects the base so the angle measure is going to be 90 degrees. We also know that the side of the triangle is 10 units so we can set up the following equation:

cos 20 = x / 10 because cos is adjacent over hypotenuse and the hypotenuse is going to be 10 in this triangle and then the adjacent is what we are trying to find or in other words the altitude.

now we start doing a little work and then turn to our calculators:

10 sin 20 = x
10(0.9396) = x
9.40 is the approximate value of x so the answer is A.

We can also do a little more math and then use sine and we will get the same answer. To use sine first we need to find the other angle measure but doing this is relatively easy.

90+20+x = 180
20+x = 90
x = 70

so we get the other angle measure to be 70 degree's.

so now our equation becomes:

sin(70) = x/10
10 sin(70) = x
10(0.9396) = x
9.4 = x