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[ here, y can be replaced with f(x) because y is a function of x ]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
A surveyor wants to find the height of a building. at a point 109.0 ft from the base of the building he sights to the top of the
building and finds the distance to be 194.0 ft. how high is the building (to the nearest tenth)?
1 answer:
Draw an illustration
We could draw an illustration of the problem by drawing a right triangle.
109 ft will be the base of the triangle, 194 ft will be the hypotenuse of the triangle, and the height of the building will be the height of the triangle.
See image attached.
Solve the problem with phytagorean theorem
For an instance, h represents the height of the building. We could find the value of h by using pythagorean theorem
a² + b² = c²
a and b act as the base and the height, c acts as the hypotenuse
in this case, we could write it as below
h² + 109² = 194²
Solve the equation
h² + 109² = 194²
h² = 194² - 109²
h² = 37,636 - 11,881
h² = 25,755
h = √25,755
h = 160.4836
To the nearest tenth
h = 160.5
The building is 160.5 ft high
We could draw an illustration of the problem by drawing a right triangle.
109 ft will be the base of the triangle, 194 ft will be the hypotenuse of the triangle, and the height of the building will be the height of the triangle.
See image attached.
Solve the problem with phytagorean theorem
For an instance, h represents the height of the building. We could find the value of h by using pythagorean theorem
a² + b² = c²
a and b act as the base and the height, c acts as the hypotenuse
in this case, we could write it as below
h² + 109² = 194²
Solve the equation
h² + 109² = 194²
h² = 194² - 109²
h² = 37,636 - 11,881
h² = 25,755
h = √25,755
h = 160.4836
To the nearest tenth
h = 160.5
The building is 160.5 ft high
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Answer:
It is an identity, proved below.
Step-by-step explanation:
I assume you want to prove the identity. There are several ways to prove the identity but here I will prove using one of method.
First, we have to know what cot and cosec are. They both are the reciprocal of sin (cosec) and tan (cot).
csc is mostly written which is cosec, first we have to write in 1/tan and 1/sin form.
Another identity is:
Therefore:
Now this is easier to prove because of same denominator, next step is to multiply 1 by sin^2x with denominator and numerator.
Another identity:
Therefore:
Hence proved, this is proof by using identity helping to find the specific identity.