Question

A tree house is being constructed with support beams that create right triangles. If the legs of the triangle created measure 2.5 ft and 3 ft, what are the angle measures of the non-right angles?

39.8 and 50.2
68.5 and 21.5
87.6 and 2.4
56.4 and 33.6

Answer 1

Answer: 39.8 and 50.2

Explanation:

Here, the triangles has the legs 2.5 ft and 3 ft.

Since, by the Pythagoras theorem,

Hypotenuses of the triangle,

`=√(2.5^2+3^2)=√(6.25+9)=√(15.25)\text{ feet}`

Now, let
`\theta_1` and
`\theta_2` are the angles opposite to the sides 2.5 and 3 respectively,

Hence, by the law of sine,

`(sin\theta_1)/(2.5)=(sin\theta_2)/(3)=(sin90^(\circ))/(√(15.25))`

When,

`(sin\theta_1)/(2.5)=(sin90^(\circ))/(√(15.25))`

`\implies sin\theta_1=(2.5)/(√(15.25))=0.64018439966`

`\implies \theta_1=39.8055710923 \approx 39.8^(\circ)`

Similarly,

`(sin\theta_2)/(3)=(sin90^(\circ))/(√(15.25))`

`\implies sin\theta_2=(3)/(√(15.25))=0.76822127959`

`\implies \theta_2=50.1944289077 \approx 50.2^(\circ)`

Hence, First option is correct.