Question

Given a triangle with b = 10, c = 11 , and A = 43°, what is the length of a? Round to the nearest tenth.

7.2

8.8

7.8

8.4

Answer 1

Option C.

Explanation:

Given: b = 10, c = 11 , and A = 43°.

Cosine formula:

`a^2=b^2+c^2-2bc\cos A`

Substitute the given values in the above formula.

`a^2=(10)^2+(11)^2-2(10)(11)\cos (43^\circ)`

`a^2=100+121-220(0.7314)`

`a^2=60.092`

Taking square root on both sides.

`a=√(60.092)`

`a=7.75619`

`a\approx 7.8`

Hence, the correct option is C.

Answer 2

You are given two sides and an angle.

Using SAS, would use the law of cosines.

a = √(10^2 + 11^2 - 2*10*11*cos(43))

a = 7.75

Round to 7.8