The first one iswhat angle does a 3.8m ladder make with the ground, if it reaches 2.1m up the wall?
The second one is A concreter uses a ramp to wheelbarrow in sand from the ground level to floor level inside a building under construction. Floor level is 75cm above ground level. if the ramp is 5.4 m long what angle, to the nearest degree, does the ramp make with the ground level?
sin theta = 2.1/3.8 = opposite/hypotenuse
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same thing
sin theta = 0.75/5.4
To find the angle in the first scenario, we can use trigonometry. The ladder forms a right triangle with the wall and the ground. The ladder's length is the hypotenuse, the distance it reaches up the wall is the opposite side, and the distance from the base of the ladder to the wall is the adjacent side.
Using the trigonometric function tangent (tan), we can find the angle:
tan(angle) = opposite/adjacent
In this case, the opposite side is 2.1m (height reached on the wall) and the adjacent side is 3.8m (length of the ladder).
So, tan(angle) = 2.1/3.8
To find the angle, we can take the inverse tangent (arctan) of the value obtained from the calculation above.
angle = arctan(2.1/3.8)
Using a calculator, the angle is approximately 30.9 degrees.
Now, let's move on to the second scenario:
Similarly, the ramp forms a right triangle with the ground and the floor level. The length of the ramp is the hypotenuse, the height difference between the floor and the ground is the opposite side, and the distance along the ground is the adjacent side.
Using the same trigonometric function tangent (tan), we can find the angle:
tan(angle) = opposite/adjacent
In this case, the opposite side is 75cm (floor level above ground) and the adjacent side is 5.4m (length of the ramp).
So, tan(angle) = 0.75/5.4
To find the angle, we can take the inverse tangent (arctan) of the value obtained from the calculation above.
angle = arctan(0.75/5.4)
Using a calculator, the angle is approximately 7.9 degrees (rounded to the nearest degree).