A hunter walks 400m Up a hill which slopes at an angle of 20 to the horizontal. Calculate,correct to the nearest metre, the:
a. horizontal distance he covered
b.vertical height through which he rises.
cool right
Cos adj =cos20°×400. =Cos20° = 400. X cos 20° =. 400.
Cos 20°. Cos 20
X = 400
0•9397
400
0•9397= 425•7
a. Well, let's do some hillarious math here! Since the hill slopes at an angle of 20 degrees, we can use some trigonometric tomfoolery. The horizontal distance covered can be found using the formula: horizontal distance = hypotenuse * cosine(angle). In this case, the hypotenuse is 400m, and the angle is 20 degrees. So, let's plug in the numbers and see what we get... *drumroll*... The horizontal distance he covered is approximately 374 meters!
b. Now, to calculate the vertical height like a comedy genius, we can use the same formula: vertical height = hypotenuse * sine(angle). Again, the hypotenuse is 400m and the angle is 20 degrees. So, let's perform some mathematical acrobatics and see the final result... *cue hilarious suspense*... The vertical height through which he rises is approximately 137 meters!
I hope these answers brought a smile to your face!
To solve this problem, we can use trigonometry. Here's how you can calculate the horizontal distance and vertical height:
a. Horizontal distance:
To find the horizontal distance, we need to find the component of the total distance that lies horizontally. We can do this by using the cosine function. The cosine of the angle is equal to the adjacent side divided by the hypotenuse.
In this case, the adjacent side is the horizontal distance, and the hypotenuse is the total distance traveled. We can set up the equation as follows:
cos(angle) = adjacent / hypotenuse
cos(20°) = adjacent / 400m
To solve for adjacent, we can rearrange the equation:
adjacent = cos(20°) * 400m
Using a calculator, evaluate the cosine of 20° and multiply it by 400m to get the horizontal distance.
b. Vertical height:
To find the vertical height, we need to find the component of the total distance that lies vertically. We can do this by using the sine function. The sine of the angle is equal to the opposite side divided by the hypotenuse.
In this case, the opposite side is the vertical height, and the hypotenuse is the total distance traveled. We can set up the equation as follows:
sin(angle) = opposite / hypotenuse
sin(20°) = opposite / 400m
To solve for the opposite (vertical height), we can rearrange the equation:
opposite = sin(20°) * 400m
Using a calculator, evaluate the sine of 20° and multiply it by 400m to get the vertical height.
By plugging in the values and evaluating the calculations, you can find the horizontal distance and vertical height. Round the answers to the nearest meter for the final values.
Answer to the question
You have a right-angled triangle with hypotenuse of 400
the horizontal distance will be the x of that triangle
cos20° = x/400
x = 400cos20°
the vertical height will be the y of that triangle
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I am sure you can take over from here