In δstu, the measure of ∠u=90°, the measure of ∠t=47°, and st = 7.2 feet. find the length of us to the nearest tenth of a foot.

Step-by-step explanation:

we know that

In the right triangle STU

The sine of angle T is equal to the opposite side angle T divided by the hypotenuse

substitute the values

Applying the trigonometry ratio, SOH, the length of US is: 5.3 feet

Recall the Trigonometry Ratio, SOH:

SOH stands for: sin ∅ = Opposite/hypotenuse

Given the following for ΔSTU:

Therefore, applying the trigonometry ratio, SOH, we have the following:

Reference angle (∅) = 47°

US = opposite = ?

ST = hypotenuse = 7.2 feet

sin 47° = US/7.2

US = (sin 47°)(7.2)

US = 5.3 feet

Learn more about trigonometry ratio on:

link

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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