The Dotson deck had a side length of 11 feet. The Engels family deck had a total area
of 118 square feet. Which deck is larger? Explain your reasoning.

Step-by-step explanation:

Given sin 30° = 1/2, to check which of the statements is correct we will apply the Pythagoras theorem to a right angled triangle shown in the attachment.

using the SOH CAH TOA trig identity on the right angled triangle, ACD gotten from the equilateral triangle ABC;

From ΔACD, AD is the hypotenuse, DC is the opposite side to the angle 30° and AC is the adjacent.

From the diagram, sin30° = opp/hyp = DC/AD

sin30° = 1/2

Taking consideration of the acute angle 60°, the opposite side to the angle will be AC and the adjacent side will be CD.

According to CAH, cos 60° = adj/hyp = CD/AD

Given CD = 1 and AD = 2

cos60° = 1/2

This shows that sin30° = cos60° = 1/2

Note that ∠CDA and ∠DAC are angles complementary. Complementary angles are angles which have its sum to be 90°