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a hiker, whose eye is 1.6 meters above ground, stands 50 meters from the base of connecting her eye and the top of the cliff and a horizontal line is 58°. draw a diagram representing the situation and find the height of the cliff

Respuesta :

abidemiokin

Answer:

80.02m

Step-by-step explanation:

Find the diagram attached. Using SOH, CAH, TOA to find the height of the cliff AC,

AC is the opposite side and BC is the adjacent

Given BC = 50m and ∠ABC = 58°

tan∠ABC = AC/BC

tan58° = AC/50

cross multiply

AC = 50tan58°

AC = 80.02m

Hence the height of the cliff is 80.02m

Ver imagen abidemiokin

Answer:

The height of the cliff is 81.6m

Step-by-step explanation:

Please see the attachment below for an illustrative diagram representing the situation.

Step-by-step explanation:

From the diagram

x = /AB/

The height of the cliff is given by ( x + 1.6m)

Considering triangle ABC which is a right-angle triangle

/AB/ is the opposite and

/BC/ is the adjacent ; /BC/ = 50m

Angle of elevation is 58°

Then, we can write that

[tex]Tan 58^{o} = \frac{/AB/}{50m}[/tex]

[tex]/AB/ = 50 (tan58^{o})\\[/tex]

[tex]/AB/ = 50 \times 1.600[/tex]

[tex]/AB/ = 80.0m[/tex]

Hence, Side /AB/ = 80.0m

Since, /AB/ = x

∴ x = 80.0 m

Recall, the height of the cliff is given by

x + 1.6m

= 80.0m + 1.6m  

= 81.6 m

Hence, the height of the cliff is 81.6m

Ver imagen Abdulazeez10

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