Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the

Question

Gemiola

1 month ago

7

Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the

top of the dam to be 26º.
Scarlett's height is 1.65 meters, so the height of the dam is () meters.

Mathematics

2 answers:

Zina [12.3K] · Answer 1 · 2026-02-27T16:47:26+03:00

Response:

The dam stands at 45.54 m tall.

Step-by-step breakdown:

Details: Scarlett is measuring the dam's height. She maintains a distance of 90 meters from the dam while observing an angle of elevation to the top of the structure at 26º. Scarlett herself is 1.65 meters high.

Query: What is the height of the dam?

Solution:

Please refer to the accompanying figure for clarification.

Scarlett's height is marked as EC= 1.65 meters

She is positioned 90 meters away from the dam, represented as DE = BC = 90 m

The angle to the dam's apex is 26º, designated as ∠BCA = 26°

Next:

The Dam's height calculates as AD = BD + AB

Here, BD equals EC = 1.65

Using trigonometric principles in triangle ABC:

$\tan \theta = \frac{\text{Perpendicular}}{\text{Base}}$

$\tan26^{\circ} = \frac{DE}{BE}$

$\tan26^{\circ} =\frac{DE}{90}$

$0.48773 \times 90=DE$

$DE=43.89$

Substituting the figures yields:

Dam's height AD = 1.65 + 43.89 = 45.54 m

Hence, the dam's height is 45.54 m.

Inessa [12.5K] · Answer 2 · 2026-02-27T16:47:45+03:00

Response:

45.54m

Step-by-step breakdown:

See the provided figure

Scarlett's height is represented as AB = 1.65 meters

She stands 90 meters away from the dam, so BE = AC = 90 m

Scarlett measures the angle of elevation to the dam's summit at 26º, which is ∠DBE = 26°

Height of the Dam = DC = EC+DE

AB = EC = 1.65

In triangle BDE

$Tan \theta = \frac{Perpendicular}{Base}$

$Tan 26^{\circ} = \frac{DE}{BE}$

$Tan 26^{\circ} = \frac{DE}{90}$

$0.48773 \times 90=DE$

$43.89=DE$

Height of the Dam = DC = 1.65 + 43.89 = 45.54 m

Therefore, the dam's height is 45.54 m.

Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the

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