Applying the cosine law, we can determine:
<span>c</span>²<span> = a</span>²<span> + b</span>²<span> - 2abcos(C) </span>
<span>where: </span>
<span>a, b, and c represent the sides of the triangle and C indicates the angle opposite to side c</span>
<span>Thus, we have:</span>
<span>150</span>²<span> = 240</span>²<span> + 200</span>²<span> - 2(240)(200)cos(C) </span>
<span>Now we solve for C</span>
<span>22,500 = 57,600 + 40,000 - 96,000cos(C) </span>
<span>22,500 - 57,600 - 40,000 = -96,000cos(C)
</span>-75,100=-96,000cos (C)
cos (C)=0.7822916
C=arc cos(0.7822916)→ C=38.53°
<span>Therefore, the direction the captain should head towards island B is
180 - 38.53 </span><span>= 141.47 degrees</span>
From a distance of 300 feet, a car approaches you at a speed of 48 feet per second. The distance d (in feet) of the car from you after t seconds can be described by the equation d=|300−48t|. At what moments does the car find itself 60 feet away from you?
Answer:
Refer to the detailed explanation below
Step-by-step explanation:
* Let’s organize the procedure to bisect angle ABC
- Angle ABC has vertex at point B and rays BA and BC
# Step 1:
- Center the compass at point B and draw an arc that crosses rays BA and BC ⇒ fifth step
# Step 2:
- Mark point D where the arc intersects ray BA and point E where it meets ray BC ⇒ third step
# Step 3:
- With the compass on point D, create an arc inside the angle ⇒ sixth step
# Step 4:
- Using the same compass width, set it on point E and draw an arc inside the angle ⇒ second step
# Step 5:
- Let point F be the intersection of the arcs from points D and E ⇒ fourth step
# Step 6:
- Draw a ray from point B through point F ⇒ first step
* This ray divides angle ABC into two equal parts
114/6=9 parts per minute. 9 parts * 15 minutes= 135 parts
