What triangle? Is there one on here?
Answer:
D
Step-by-step explanation:
Recall that the area of a triangle is given by:
In this case, the base is <em>x</em> and the height is <em>y</em>. Hence:
We can write the following ratios:
Solve for <em>x</em> and <em>y</em>:
Substitute:
And simplify. Hence:
In conclusion, our answer is D.
Answer:
(1) 20%
Step-by-step explanation:
→ Find the difference in price
200 - 160 = 40
→ Divide difference by original price
40 ÷ 200 = 0.2
→ Multiply the answer by 100
0.2 × 100 = 20%
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.
Your equation: 4x² - 100 = 0
Factor the left side: (2x + 10) · (2x - 10) = 0
This equation is true if either factor is zero.
-- One factor: 2x + 10 = 0
Divide each side by 2: x + 5 = 0
Subtract 5 from each side: x = -5 .
-- The other factor: 2x - 10 = 0
Divide each side by 2: x + 5 = 0
Add 5 to each side: x = 5 .
