Answer: 4.5 miles
Explanation:
When you draw the situation you find two triangles.
1) Triangle to the east of the helicopter
a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°
b) hypotensue = distance between the high school and the helicopter
c) opposite-leg to angle 20° = heigth of the helicopter
d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x
2) triangle to the west of the helicopter
a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°
b) distance between the helicopter and the elementary school = hypotenuse
c) opposite-leg to angle 62° = height of the helicopter
d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x
3) tangent ratios
a) triangle with the helicpoter and the high school
tan 20° = Height / x ⇒ height = x tan 20°
b) triangle with the helicopter and the elementary school
tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°
c) equal the height from both triangles:
x tan 20° = (5 - x) tan 62°
x tan 20° = 5 tan 62° - x tan 62°
x tan 20° + x tan 62° = 5 tan 62°
x (tan 20° + tan 62°) = 5 tan 62°
⇒ x = 5 tant 62° / ( tan 20° + tan 62°)
⇒ x = 4,19 miles
=> height = x tan 20° = 4,19 tan 20° = 1,525 miles
4) Calculate the hypotenuse of this triangle:
hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²
hipotenuse = 4.46 miles
Rounded to the nearest tenth = 4.5 miles
That is the distance between the helicopter and the high school.
Answer:
3, 12, 27 and 300
Step-by-step explanation:
Plug n as 1, 2, 3 and 10.
3(1)² = 3
3(2)² = 12
3(3)² = 27
3(10)² = 300
Answer:
a° = 58°
b° = 48°
c = 74°
d° = 122°
Step-by-step explanation:
<em>Angles on a straight line add up to 180°</em>
58° + d° = 180°
d° = 180° - 58° = 122°
<em>Alternate angles are equal.</em>
a° = 58°
<em>Angles in a triangle add up to 180°.</em>
48° + 58° + c° = 180°
106° + c° = 180°
c° = 180° - 106° = 74°
<em>Angles on a straight line add up to 180°</em>
74° + 58° + b° = 180°
132° + b° = 180°
b° = 180° - 132° = 48°
When you simplify the square root of a number, you are looking for factors of the number that are perfect squares that you can remove from under the radical. For example sq root of 8... it's not a perfect square but factors of 8 include 2 x 4... 4 is a perfect square so we can take it out of the radical by taking it's square root. Now you are left with 2* sq root of 2.
For sq root of 48
48 = 12 x 4
12 = 3x4 so we can say 48 = 3x4x4
so... sq root 48 = sq root 3x4x4
we have two 4's under the radical. Sq root x^2 = x so sq root 4^2 is 4
Pull it out from the radical and we are left with 4 * sq root 3
Answer:
110 R 5
Step-by-step explanation:
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