Answer:
The height of the cliff CD is approximately 539.76 m
Step-by-step explanation:
The given parameters are;
The first angle of elevation with which the captain sees the person on the cliff = 61°
The second angle of elevation with which the captain sees the person on the cliff after moving 92 m closer to the cliff = 69°
The angle made by the adjacent supplementary angle to the second angle of elevation = 180° - 69° = 111°
∴ Whereby, the rays from the first and second angle of elevation and the distance the ship moves closer to the cliff forms an imaginary triangle, we have;
The angle in the imaginary triangle subtended by the distance the ship moves closer to the cliff = 180° - 111° - 61° = 8°
By sine rule, we have;
AB/(sin(a)) = BC/(sin(c))
Which gives;
92/(sin(8°)) = BC/(sin(61°))
BC = (sin(61°)) × 92/(sin(8°)) ≈ 578.165 m
BC ≈ 578.165 m
The height CD = BC × sin(69°)
∴ The height of the cliff CD = 578.165 m × sin(69°) ≈ 539.76 m.
The height of the cliff CD ≈ 539.76 m.
Answer:
70%
Step-by-step explanation:
Since it can't go over 100%, and our numbers are 7 and 3, they are 70% and 30%, which add up to 100%.
Answer:
Explanation:
<u>1. Calculate the average speed of train B</u>
- 60mph = 3/4 (s) ⇒ s = 60 (4/3) mph = 80 mph
<u>2. Build a table</u>
When the two trains meet:
Train Average speed Distance time (distance/average speed)
mph
A 60 x x/60
B 80 240 - x (240 - x) / 80
<u>3. Write the equation</u>
The time, when the two trains meet, is the same for both trains:
<u>4. Calculate the time:</u>
- x/60 = 102.86 / 60 = 1.7 hours
The two trains will meet after 1.7 hours
You need to use Pythagoras’ Theorem.
A² + B² = c² and c is the hypotenuse of the right angled triangle.
The height of the tower (5 feet) is A and the distance from the end of the cable and the base of the tower (12 feet) is B. The length of ONE cable is c. So:
A² + B² = c²
5² + 12² = c²
25 + 144 = c²
169 = c²
13 = c. This is the length of one cable.
3 x 13 = 39 therefore the total length of the cables is 39 feet.
25
Answer:
area = 18x² + 63x + 55 square units
Second-degree trinomial.
Step-by-step explanation:
area = (3x+5)(6x+11) = 18x² + 63x + 55 square units
Second-degree trinomial.
