Given an IVP

5) In the figure, triangle ABC is a right triangle at B. If CD = 15, find BC to the nearest tenth.

ycow [4]

Answer:

BC ≈ 4.0

Step-by-step explanation:

∠ DCA = 180° - 70° = 110° ( adjacent angles )

∠ DAC = 180° - (30 + 110)° ← sum of angles in triangle

∠ DAC = 180° - 140° = 40°

Using the Sine rule in Δ ACD to find common side AC

$\frac{AC}{sin30}$ = $\frac{15}{sin40}$ ( cross- multiply )

AC × sin40° = 15 × sin30° ( divide both sides by sin40° )

AC = $\frac{15sin30}{sin40}$ ≈ 11.668

Using the cosine ratio in right triangle ABC

cos70° = $\frac{adjacent}{hypotenuse}$ = $\frac{BC}{AC}$ = $\frac{BC}{11.668}$ ( multiply both sides by 11.668 )

11.668 × cos70° = BC , then

BC ≈ 4.0 ( to the nearest tenth )

6 0

2 years ago

a survey conducted in a school showed that 65% of the students walked to school. The remaining students took buses to school. Th

Feliz [49]

I fear that there is an error copying your assignment.
65% of the students walked. Are all of the other students on buses? Are there both public buses AND private buses?
Assuming that you need to know BOTH kinds of buses, try this:

65% of the students walked, so since 100% - 65% = 35% then this means that 35% of the students were on buses.
Since we know that there are 360 more walkers than bus riders, then one equation we know is: 65% of S = 360 + 35% of S (let S = total # of students)
.65 S = 360 + .35 S
 - .35 S = - .35 S Subtract .35 S from both sides
 .30 S = 360 Divide both sides by .30 (or .3)
.30 .30
S = 1,200 so we know that this is the total number of students, but that is not what was asked.
They want to know how many are on buses and specifically how many are on public buses, if I read this correctly.
Since the walkers = 65% of 1,2000 and we know of means TIMES, then
.65 (1,200) = 780 walkers
1,200 total students minus 780 walkers = 420 bus riders

Now, if there is not a misprint and we really have to figure out the public bus riders as compared to the private bus riders, then remember the ratio from above in the question: 4 bus: 3 public buses
Now if I read this right, that means that 3/4ths of the bus riders were on public buses
so 3/4 of 420 means 3/4 times 420 = 3 times 105 = 315 public bus riders (which coincidentally leaves 105 private bus riders, but since they are private we don't know much about them. Ha-Ha..... I made a lame joke.)

So your answer is 315 public bus riders

5 0

3 years ago

Read 2 more answers

What is the formula for the area of a triangle?

SashulF [63]

The formula to find the area of a triangle is :

1/2 base*height

For instance:

base=4 cm

height=5cm

area of traingle=1/2*b*h

 =1/2*4*5

 =10cm^2

Hope it helps...

Good luck on your assignment

6 0

2 years ago

Simplify the expression x - (12 – 5x)

san4es73 [151]

Answer:

6x-12

Step-by-step explanation:

hope this helps

3 0

2 years ago

Read 2 more answers

What is the area of this triangle? _units²

MrRissso [65]

The area of the triangle is 4 units²

<h3>What is the area of a triangle?</h3>

The area of a triangle is the half the base multiplied with the height of that triangle

Area = 1/ 2 × b × h

From the figure given,

base = 7 - 3 = 4 units

height = 4 - 2 = 2 units

Area = 1/ 2 × 4 × 2

Area = 1/ 2 × 8

Area = 4 units²

Thus, the area of the triangle is 4 units²

Learn more about a triangle here:

brainly.com/question/1475130

#SPJ1

3 0

1 year ago