Rationalize and simplify completely.
1 answer:
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Answer:
The height of the hill = h = 580.7 feet
Step-by-step explanation:
Let height of the hill = h
From the triangle A B D
Tan 22 =
⇒ AB = h & B D = y + 700
⇒ Tan 22 = ------------(1)
From triangle ABC
Tan 38 =
⇒ AB = h & BC = y
⇒ Tan 38 = ------------------(2)
⇒ h = y tan 38 -----------------(3)
Put the value of h from equation (3) into equation (1) we get
⇒ (tan 22) × (y + 700) = y × tan 38
⇒ 0.40 y + 282.82 = y × 0.78
⇒ y = 742.12 feet -----------------(4)
Put this value of y in equation 3 we get
⇒ h = 742.12 × tan 38
⇒ h = 580.7 feet
This is the height of the hill.
Answer:
b.12
Step-by-step explanation:
<u>Key skills needed: Interior Angle Measure Theorem, Equation Creation</u>
1) First, we need to classify this shape. It has 7 sides, which means that we can use the Interior angle Theorem to find out the sum of all the interior angle measures
The theorem is:
S is the sum of all interior angle measures
n is the number of sides of the polygon
2) With this, we can plug in 7 for "n" (Since the figure has 7 sides) and get:
--->
---> (7-2) is 5 since 7 - 2 = 5 so -->
---> 5(180) is the same as 5 x 180 which is 900 so -->
This means that the sum of all interior angles is 900 degrees.
3) Now, we have to find out the sum of all the angles that they gave us so:
--->
The left side is the sum of all interior angles in the shape, and the right side is what the sum should be when expressed as a number.
4) We have to combine all like terms on the left side:
--->
--->
5) This means that --->
Subtract 288 from both sides and get:
---> (900-288 = 612)
Then divide by 51 from both sides and get:
---> (612 ÷ 51 = 12)
Therefore b.12 is your answer.
<em>Hope you understood and have a nice day!! :D</em>