Answer: 39.8 and 50.2
Step-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 [/tex]
[tex]\implies \theta_2=50.1944289077
\approx 50.2^{\circ}[/tex]
Hence, First option is correct.
