Here we don't know the length of the hypo, but do have measures of both legs of this right triangle: x and 40 yd.
Use the tangent function to determine the value of x:
x
--------- = tan 62 degrees. Solving for x: x = (40 yd)(tan 62 deg).
40 yd can you evaluate this yourself?
Answer:
Step-by-step explanation:
Use the slope formula
(x2-x1)/(y2/y1)
substitute the values
(1-10)/(9-7)
solve
-9/-2
simplify
9/2 or 4.5
So the object of this problem is to find out the value of d.
To do this, first think about 5 + 3. This equals 8, right? So the value of d times 4 has to equal 8.
No other number besides 2 would make sense. 2 would equal d because 4 x 2 is 8, and 5 + 3 is 8.
So you would write the answer as:
5+3=4(2)
By definition of tangent,
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
Recall the double angle identities:
sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)
cos(2<em>θ</em>) = cos²(<em>θ</em>) - sin²(<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
where the latter equality follows from the Pythagorean identity, cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1. From this identity we can solve for the unknown value of sin(<em>θ</em>):
sin(<em>θ</em>) = ± √(1 - cos²(<em>θ</em>))
and the sign of sin(<em>θ</em>) is determined by the quadrant in which the angle terminates.
<em />
We're given that <em>θ</em> belongs to the third quadrant, for which both sin(<em>θ</em>) and cos(<em>θ</em>) are negative. So if cos(<em>θ</em>) = -4/5, we get
sin(<em>θ</em>) = - √(1 - (-4/5)²) = -3/5
Then
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
tan(2<em>θ</em>) = (2 sin(<em>θ</em>) cos(<em>θ</em>)) / (2 cos²(<em>θ</em>) - 1)
tan(2<em>θ</em>) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)
tan(2<em>θ</em>) = 24/7
Answer:
x intercept: (4,0)
y intercept: (0,2 1/2)
Step-by-step explanation:
