Katherine has a points card for a movie theater.
1 answer:
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Answer:
84.5 m
Step-by-step explanation:
It is often helpful to draw a diagram for word problems involving geometric relationships. One for this problem is shown below.
The mnemonic SOH CAH TOA reminds you of the relationship between sides of a right triangle:
Tan = Opposite/Adjacent
Here we're given angles of depression measured from the horizontal (as shown in the diagram), but it is more convenient to use angles measured from the vertical. In particular, ∠BAO is the complement of 60°, and its tangent is the ratio OB/OA:
tan(30°) = OB/OA
OB = (200 m)·tan(30°) ≈ 115.47 m . . . . . . multiply by OA, use OA=200 m
Likewise, we have ...
OC = (200 m)·tan(45°) = 200 m
Then the width of the river is the difference between these values:
BC = OC -OB = 200 m - 115.47 m = 84.53 m
Answer:
y = 5
Step-by-step explanation:
Calculate the slope m using the slope formula
m =
with (x₁, y₁ ) = (7, 5) and (x₂, y₂ ) = (- 9, 5)
m = =
= 0
This means the line is horizontal and parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (7, 5) and (- 9, 5) with y- coordinates 5, thus
y = 5 ← equation of line