Help please

4) Solve ∆ABC, a = 2.5 cm, c = 3.6 cm, and ∠A = 43°. Begin by sketching and labelling

mezya [45]

The length of b and angle B and C are 3cm, 45 degrees and 79 degrees respectively.

<h3>How to determine the parameters</h3>

To determine the angles and length of sides, we use the sine rule

The sine rule is thus:

$\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}$

Given;

a = 2. 5cm

c = 3. 6cm

∠A = 43°

Let's find angle C

$\frac{sin 43}{2. 5} = \frac{sin C}{3. 6}$

cross multiply

0. 682 × 3. 6 = sin C × 2. 5

sin C = 2. 4552/ 2. 5

C = $sin^-^1(0. 982)$

C = 79°

To find length of b

$b= \sqrt{c^2 - a^2}$

substitute the values

$b = \sqrt{3.6^2 - 2. 5^2}$

$b = \sqrt{6. 71}$

b = 2. 59 cm

b = 3cm

To find angle B, we have

$\frac{sin 43}{2. 5} = \frac{sin B}{2. 59}$

cross multiply

0. 682 × 2. 59= sin B × 2. 5

sin B = 0. 7065

$B = sin^-^1(0. 7065)$

B = 45°

Hence, the length of b and angle B and C are 3cm, 45 degrees and 79 degrees respectively.

Learn more about sine rule here:

brainly.com/question/12827625

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8 0

1 year ago

If b = 10 then a = 5<br><br> what id 2b+5a

MrRa [10]

2(10) +5(5)= 45

b=10 a=5

Plug in the values b and a.

7 0

2 years ago

Please help I dont know how

Tresset [83]

Answer:

y = 1/2x + 5

Step-by-step explanation:

The line has a slope of one half. If you look at the dots made, take a look at the dot on the y-axis. Then, if you move up one space from that point, and move two spaces to the right of the point, you reach the second dot. This determines the slope which would be written as 1/2x. Then, if you look back to where the line passes through the y axis, you'll see it landed on positive five. This means 5 will be added to the end of the equation. So, y equals the slope plus the y-intercept. y = 1/2x + 5

5 0

3 years ago

Read 2 more answers

From a deck of five cards numbered 2, 4, 6, 8, and 10, respectively, a card is drawn at random and replaced. this is done three

Serga [27]

Since the sum of the numbers on the three draws is 12, if we want the card numbered 2 to be drawn exactly two times, the third card can only be numbered 8. In fact, $2+2+8 = 12$ , and there are no other possibilities, unless you consider the various permutations of the terms.

So, we have three favourable cases: we can draw 2,2,8, or 2,8,2, or 8,2,2. This are the only three cases where the card numbered 2 is drawn exactly two times, and the sum of the number on the three draws is 12.

Now, the question is: we have three favourable cases over how many? Well, we have 5 possible outcomes with each draws, and the three draws are identical, because we replace the card we draw every time.

So, we have 5 possible outcomes for the first draw, 5 for the second and 5 for the third. This leads to a total of $5 \times 5 \times 5 = 5^3 = 125$ possible triplets.

Once we know the "good" cases and the total number of possible cases, the probability is simply computed as

$P = \cfrac{\text{number of favourable cases}}{\text{number of all possible cases}} = \cfrac{3}{125}$

3 0

3 years ago

A trough has ends shaped like isosceles triangles, with width 5 m and height 7 m, and the trough is 12 m long. Water is being pu

Svet_ta [14]

Answer:

$\dfrac{dh}{dt}=21 \text{m/min}$

the rate of change of height when the water is 1 meter deep is 21 m/min

Step-by-step explanation:

First we need to find the volume of the trough given its dimensions and shape: (it has a prism shape so we can directly use that formula OR we can multiply the area of its triangular face with the length of the trough)

$V = \dfrac{1}{2}(bh)\times L$

here L is a constant since that won't change as the water is being filled in the trough, however 'b' and 'h' will be changing. The equation has two independent variables and we need to convert this equation so it is only dependent on 'h' (the height of the water).

As its an isosceles triangle we can find a relationship between b and h. the ratio between the b and h will be always be the same:

$\dfrac{b}{h} = \dfrac{5}{7}$