Question

Pls help lol my grade’s a 62 rn & grades are almost due !

Answer 1

170 meters

Explanation:

The three sides of a right triangle are named hypotenuse, adjacent side and opposite side and the angle the adjacent side makes with they hypotenuse is θ (see Figure 1)

In this description the terms
Opposite --> side opposite to the angle θ

Adjacent --> side adjacent to the angle θ

Hypotenuse --> longest side of the right triangle

The relationship between the ratio of the shorter sides and and the angle θ in the figure is given by the formula


`\mathrm {\tan(\theta) = (Opposite \; side)/(Adjacent \;side)}`

We can view the Eiffel Tower as the opposite side, the distance from the base to the surveyor location as the adjacent side (see the second figure)

If we let h = height of the Eiffel Tower in meters , opposite side length = h m

The adjacent side length = 202 meters

The angle θ = 40°

Applying the tan formula we get

`\tan(40^\circ) = (h)/(202)\\\\\textrm{Multiplying both sides by 202, }\\202 \tan(40^\circ) = h\\\\\\h = 202 \tan(40^\circ) \\\textrm{Using a calculator we get}\\\\h = 169.5\; meters`

Rounded to the nearest meter, the height = 170 meters

Answer 2

The triangle in the image is a right triangle. We are given a side and an angle, and asked to find another side. Therefore, we should use a trigonometric function.

Trigonometric Functions: SOH-CAH-TOA

---sin = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent

In this problem, looking from the angle, we are given the adjacent side and want to find the opposite side. This means we should use the tangent function.

tan(40) = x / 202

x = tan(40) * 202

x = 169.498

x (rounded) = 169 meters

Answer: the tower is 169 meters tall

Hope this helps!