The distance from an observer on the plain to the top of a nearby mountain is 5.3km, and the angle between this line and the horizontal is 8.4 degrees. How tall is the mountain?
5.3sin(8.4)
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To find the height of the mountain, we can use trigonometry. We know the distance from the observer to the mountain (5.3 km) and the angle between this line and the horizontal (8.4 degrees).
Let's assume that the height of the mountain is represented by "h".
Using the trigonometric relationship "tan(angle) = opposite/adjacent":
tan(8.4°) = h/5.3 km
To isolate "h", we can multiply both sides of the equation by 5.3 km:
5.3 km * tan(8.4°) = h
Calculating the right side of the equation:
h ≈ 0.931 km
Therefore, the height of the mountain is approximately 0.931 km.
To find the height of the mountain, we can use trigonometry. In this case, we'll use the tangent function.
Let's label the distance from the observer to the top of the mountain as the adjacent side (A) and the height of the mountain as the opposite side (O). The angle between the line and the horizontal is 8.4 degrees. We know the tangent of an angle is equal to the opposite side divided by the adjacent side. Mathematically, this can be expressed as:
tan(angle) = O / A
Rearrange the equation to solve for O:
O = tan(angle) * A
Now, we can substitute the given values:
O = tan(8.4 degrees) * 5.3 km
To evaluate this expression, you can use a calculator or a mathematical software that supports trigonometric functions. Plugging the values into the equation, we get:
O ≈ 0.1487 * 5.3 km
Calculating the product:
O ≈ 0.787 km
Hence, the height of the mountain is approximately 0.787 km or 787 meters.