A
using the Cosine rule in ΔSTU
let t = SU, s = TU and u = ST, then
t² = u² + s² - (2us cos T )
substitute the appropriate values into the formula
t² = 5² + 9² - (2 × 5 × 9 × cos68° )
= 25 + 81 - 90cos68°
= 106 - 33.71 = 72.29
⇒ t = ≈ 8.5 in → A
A gear makes 50 revolutions each minute. It can be represented by the equation r-50t, where r is the total revolutions and t is
2 answers:
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From my own solution, my answer is closest to D<span>. 1951 yd; 27°
</span><span>
The boat is 1951 yards away from the observer in tower B. The angle of depression to the boat from Tower B is 27</span>°.<span>
Pls. see my attachment.
In it I divided the big triangle into two small right triangles.
I solved for the common leg of the right triangles by using sin theta formula. sin </span>θ = opposite / hypotenuse
<span>
sin 35</span>° = opposite / 1538 yd
<span>sin 35</span>° * 1538 yd = opposite
<span>882.16 yd = opposite
From there, I used the Pythagorean theorem to solve for the missing side which is part of the 3,000 yd measure.
I got the measure of 1,259.86 yards. The remaining measure of 1,740.14 is the side of the other right triangle.
Still using Pythagorean Theorem, I used the measurement of the known side of the 2nd right triangle to solve for its hypotenuse which was 1,950.97 or 1,951 yards.
With regards to the angle of depression, I used this formula:
tan(y) = opposite / adjacent
tan(y) = 1538 yd / 3000 yd
tan(y) = 0.513
y = 0.513/tan
y = 27.14</span>°<span>
</span>
</span><span>
The boat is 1951 yards away from the observer in tower B. The angle of depression to the boat from Tower B is 27</span>°.<span>
Pls. see my attachment.
In it I divided the big triangle into two small right triangles.
I solved for the common leg of the right triangles by using sin theta formula. sin </span>θ = opposite / hypotenuse
<span>
sin 35</span>° = opposite / 1538 yd
<span>sin 35</span>° * 1538 yd = opposite
<span>882.16 yd = opposite
From there, I used the Pythagorean theorem to solve for the missing side which is part of the 3,000 yd measure.
I got the measure of 1,259.86 yards. The remaining measure of 1,740.14 is the side of the other right triangle.
Still using Pythagorean Theorem, I used the measurement of the known side of the 2nd right triangle to solve for its hypotenuse which was 1,950.97 or 1,951 yards.
With regards to the angle of depression, I used this formula:
tan(y) = opposite / adjacent
tan(y) = 1538 yd / 3000 yd
tan(y) = 0.513
y = 0.513/tan
y = 27.14</span>°<span>
</span>