Answer:
[tex] 60.8^\circ [/tex]
Step-by-step explanation:
First, let's check side lengths.
Using the Pythagorean theorem we can find the length of the other side of the rectangle.
a^2 + b^2 = c^2
4.2^2 + b^2 = 8.6^2
b^2 = 56.32
b = 7.5
The other side of the rectangle measures 7.5 cm, so now we know that 4.2 cm is indeed the shorter side of the rectangle.
For the angle in question, the 4.2 cm side is the adjacent leg.
The diagonal of 8.6 cm is the hypotenuse.
The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.
[tex] \cos \alpha = \dfrac{adj}{hyp} [/tex]
[tex] \cos \alpha = \dfrac{4.2~cm}{8.6~cm} [/tex]
[tex] \alpha = \cos^{-1} \dfrac{4.2~cm}{8.6~cm} [/tex]
[tex] \alpha = 60.8^\circ [/tex]
