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 50.268.5 and 21.5 87.6 and 2.4 56.4 and 33.6

Accepted Solution

Answer: 39.8 and 50.2Step-by-step explanation:Here, the triangles has the legs 2.5 ft and 3 ft.Since, by the Pythagoras theorem,Hypotenuses of the triangle,[tex]=\sqrt{2.5^2+3^2}=\sqrt{6.25+9}=\sqrt{15.25}\text{ feet}[/tex]Now, let [tex]\theta_1[/tex] and [tex]\theta_2[/tex] are the angles opposite to the sides 2.5 and 3 respectively,Hence, by the law of sine,[tex]\frac{sin\theta_1}{2.5}=\frac{sin\theta_2}{3}=\frac{sin90^{\circ}}{\sqrt{15.25}}[/tex]When,[tex]\frac{sin\theta_1}{2.5}=\frac{sin90^{\circ}}{\sqrt{15.25}}[/tex][tex]\implies sin\theta_1=\frac{2.5}{\sqrt{15.25}}=0.64018439966 [/tex][tex]\implies \theta_1=39.8055710923 \approx 39.8^{\circ}[/tex]Similarly,[tex]\frac{sin\theta_2}{3}=\frac{sin90^{\circ}}{\sqrt{15.25}}[/tex][tex]\implies sin\theta_2=\frac{3}{\sqrt{15.25}}=0.76822127959 Β [/tex][tex]\implies \theta_2=50.1944289077 \approx 50.2^{\circ}[/tex]Hence, First option is correct.