138k views
5 votes
Triangle ABC is given where MLA = 33°, a = 15 in, and the height, h, is 9 in. How many distinct triangles can be made with the given measurements? Please help :(

Triangle ABC is given where MLA = 33°, a = 15 in, and the height, h, is 9 in. How-example-1
User Warunanc
by
7.9k points

1 Answer

6 votes

Answer:

One triangle

Explanation:

step 1

Find the measure of side AC

In the right triangle of the left


sin(33^o)=(9)/(AC) ----> by SOH (opposite side divided by the hypotenuse)


AC=(9)/(sin(33^o))=16.5\ in

step 2

Find the measure of angle B

Applying the law of sines


(a)/(Sin(A))=(b)/(Sin(B))

substitute the given values


(15)/(Sin(33^o))=(16.5)/(Sin(B))


Sin(B)=(16.5)/(15)Sin(33^o)=0.60


B=sin^(-1)(0.60)= 36.87^o

step 3

Find the measure of angle C

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

so


33^o+36.87^o+ C=180^o


C=110.13^o

step 4

Find the measure of side AB

Applying the law of sines


(a)/(Sin(A))=(c)/(Sin(C))

substitute the given values


(15)/(Sin(33^o))=(c)/(Sin(110.13^o))


c=15(Sin(110.13^o))/(Sin(33^o))=25.9\ m

Each measure of the ABC triangle can only have one value, therefore only one triangle can be make with the given measures

User Bedo
by
7.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories