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3 years ago

Two angles of a triangle are 30°and 80°. Find the third angle.

Mathematics

1 answer:

stiv31 [10]3 years ago

7 0

Answer:

The third angle of the triangle is 70°.

Step-by-step explanation:

The two angles of a triangle (say Δ ABC) are given to be 30° and 80°.

We have to find the third angle.

Let us assume that ∠ A = 30° and ∠ B = 80°, then we have to find ∠ C.

Now, we know that, ∠ A + ∠ B + ∠ C = 180° {Property of a triangle}

⇒ 30° + 80° + ∠ C = 180°

⇒ ∠ C = 180° - 30° - 80° = 70°

Therefore, the third angle of the triangle is 70°. (Answer)

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3 years ago

The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.21 minutes and a st

madam [21]

Answer:

4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

Since Z > -2 and Z < 2, this outcome is not considered unusual.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If $Z \leq 2$ or $Z \geq 2$ , the outcome X is considered to be unusual.

In this question:

$\mu = 8.21, \sigma = 1.9$

Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

This is the pvalue of Z when X = 5. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{5 - 8.21}{1.9}$

$Z = -1.69$

$Z = -1.69$ has a pvalue of 0.0455.

4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.

Since Z > -2 and Z < 2, this outcome is not considered unusual.

8 0

3 years ago

Solve for x. Round to the nearest tenth, if necessary.

e-lub [12.9K]

Answer:

$\boxed {\boxed {\sf x \approx 1.9}}$

Step-by-step explanation:

We are asked to find x, a missing side in a triangle.

This is a right triangle because there is a small square in the corner representing a 90 degree or right angle. Therefore, we can use right triangle trigonometry. The three main functions are:

sinθ= opposite/hypotenuse
cosθ= adjacent/hypotenuse
tanθ= opposite/adjacent

Examine the triangle. We will use angle S, measuring 54 degrees, for theta. Side QR, measuring x, is opposite angle S. Side QS, measuring 2.3, is the hypotenuse because it is opposite the right angle. Since we have the opposite and hypotenuse, we will use sine.

$sin \theta = \frac {opposite}{hypotenuse}$

θ= 54
opposite= x
hypotenuse = 2.3

$sin (54)= \frac{ x}{2.3}$

We are solving for x, so we must isolate the variable. It is being divided by 2.3 The inverse operation of division is multiplication, so we multiply both sides by 2.3

$2.3* sin (54)= \frac{x}{2.3}*2.3$

$2.3* sin (54)=x$

$2.3*0.8090169944=x$

$1.860739087 =x$

Round to the nearest tenth. The 6 in the hundredth place to the right tells us to round the 8 up to a 9.

$1.9 \approx x$

x is approximately 1.9

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3 years ago