Question

Trevor, Robert, and Maurice made some paper airplanes and want to see how far they will fly. The distance from Trevor to Robert is 13.5 feet. The distance from Robert to Maurice is 14.2 feet. The distance from Maurice to Trevor is 6.6 feet. Find the measures of the three angles in the triangle.

a. m∠T=82.2

, m∠R=27.4 , m∠M=70.4

b. m∠T=27.4 , m∠R=70.4 , m∠M=82.2

c. m∠T=70.4 , m∠R=82.2 , m∠M=27.4

d. m∠T=60 , m∠R=60 , m∠M=60

Answer 1

a. m∠T=82.2, m∠R=27.4, m∠M=70.4

Explanation:

Let T, R and M represent the position of Trevor, Robert, and Maurice respectively,

Given,

TR = 13.5 feet,

RM = 14.2 feet,

TM = 6.6 feet,

Since, TRM forms a triangle, ( because sum of any two sides is greater than third side )

By the law of cosine,

`TR^2=RM^2+TM^2-2* RM* TM* cos M`

`\implies cos M=(RM^2+TM^2-TR^2)/(2* RM* TM)`

By substituting the values,

`cos M=(14.2^2+6.6^2-13.5^2)/(2* 14.2* 6.6)`

`cos M=(62.95)/(187.44)`

`\implies m\angle M=cos^(-1)((62.95)/(187.44))=70.3763251924\approx 70.4^(\circ)`

Similarly,

`cos R=(TR^2+RM^2-TM^2)/(2* TR* RM)`

`=(13.5^2+14.2^2-6.6^2)/(2* 13.5* 14.2)`

`=(340.33)/(383.4)`

`\implies m\angle R=cos^(-1)((340.33)/(383.4))=27.4189643117\approx 27.4^(\circ)`

`cos T=(TR^2+TM^2-RM^2)/(2* TR* TM)`

`=(13.5^2+6.6^2-14.2^2)/(2* 13.5* 6.6)`

`=(24.17)/(178.2)`

`\implies m\angle T=cos^(-1)((24.17)/(178.2))=82.2047104959\approx 82.2^(\circ)`

Hence, option 'a' is correct.

Answer 2

a. m∠T=82.2, m∠R=27.4, m∠M=70.4