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Yuki888 [10]
3 years ago
11

The angles in a triangle are in the ratio 1:2:3. Show that this triangle is a right-angled triangle. The hypotenuse of the trian

gle is 19 cm long. Calculate the length of the shortest side in the triangle

Mathematics
1 answer:
natita [175]3 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

(a)

Sum the parts of the ratio , 1 + 2 + 3 = 6 parts

Divide sum of angles in a triangle by 6 to find the value of one part of the ratio.

180° ÷ 6 = 30° ← value of 1 part of the ratio

2 parts = 2 × 30° = 60°

3 parts = 3 × 30° = 90°

Since there is an angle of 90° then the triangle is right.

(b)

The shortest side is the side opposite the smallest angle of 30°

Using the sine ratio and the exact value

sin30° = \frac{1}{2} , then

sin30° = \frac{opp}{hyp} = \frac{opp}{19} = \frac{1}{2} ( cross- multiply )

2 opp = 19 ( divide both sides by 2 )

opp = 9,5

Shortest side in the triangle is 9.5 cm

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What’s the least common denominator for 1/6 and 7/8?
Alexandra [31]

Answer:

24

Step-by-step explanation:

Here's how we construct the LCD:

Factor the denominators 6 and 8:  6 = 2*3 and 8 = 2*2*2

The LCD involves 2*2*2 as well as 3:

LCD:  2*2*2*3 = 24.  Note that 24 is divisible by both 6 and 8.  There is no smaller LCD that is divisible by 6 and 8 both.

7 0
3 years ago
What is the solution to the equation 3 x+ 2 = -x-57<br> X=-8<br> o x=-7<br> o x=7<br> O X=8
luda_lava [24]

Answer:

x = -59/4

Step-by-step explanation:

3 x+ 2 = -x-57

Add x to each side

3 x+x+ 2 = -x+x-57

4x+2 = -57

Subtract 2 from each side

4x +2-2 = -57-2

4x = -59

Divide each side by 4

4x/4 = -59/4

x = -59/4

4 0
3 years ago
Read 2 more answers
Two chemists working for a chicken fast-food company, have been producing a very popular sauce. Let’s call then Jesse and Mr. Wh
a_sh-v [17]

Answer:

Check the explanation

Step-by-step explanation:

Let \overline{x} and \overline{y} be sample means of white and Jesse denotes are two random variables.

Given that both samples are having normally distributed.

Assume \overline{x} having with mean \mu_{1} and \overline{y} having mean \mu_{2}

Also we have given the variance is constant

A)

We can test hypothesis as

H0: \mu_{1} =  \mu_{2}H1: \mu_{1} > \mu_{2}

For this problem

Test statistic is

T=\frac{\overline {x}-\overline {y}}{s\sqrt{\frac {1}{n1} +\frac{1}{n2}}}

Where

s=\sqrt{\frac{(n1-1)*s1^{2}+(n2-1)*s2^{2}}{n1+n2-2}}

We have given all information for samples

By calculations we get

s=2.41

T=2.52

Here test statistic is having t-distribution with df=(10+7-2)=15

So p-value is P(t15>2.52)=0.012

Here significance level is 0.05

Since p-value is <0.05 we are rejecting null hypothesis at 95% confidence.

We can conclude that White has significant higher mean than Jesse. This claim we can made at 95% confidence.

3 0
3 years ago
Please please help me!!!! :)
kifflom [539]

Answer:

Measure of ∠5 is 142°

Step-by-step explanation:

We are given that, Lines L and M are parallel.

As, the third line is intersecting both line L and M.

<em>We know that, 'The opposite angles formed by the intersecting lines are equal'.</em>

Since, the sum of the four angles formed by the third line and M is 360°.

So, we get,

∠1 + ∠6 + ∠7 + 38 = 360°

i.e. 2∠1 + 2×38°  = 360°

i.e. 2∠1 = 360° - 76°

i.e. 2∠1 = 284°

i.e. ∠1 = 142°

Thus, ∠1 = ∠7 = 142°

Since, L and M are parallel.

So, ∠3 = ∠5 = 142°

Hence, we get that measure of ∠5 is 142°.

3 0
3 years ago
3/4 + 5/6? What is the equation.
Virty [35]
The answer to your question is 1 7/12
8 0
3 years ago
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