Plz help 15 points And brainliest

In the triangle shown we can find the angle θ as follows calculator

Xelga [282]

Given a right triangle with hypothenus of measure 34, the side opposite the angle θ of measure 30, and the side adjacent the angle theta of measure 16.

$\sin\theta= \frac{opposite}{hypothenuse} = \frac{30}{34} = \frac{15}{17} \\ \\ \Rightarrow \theta=\sin^{-1}\left( \frac{15}{17} \right) \\ \\ \\ \cos\theta= \frac{adjacent}{hypothenuse} = \frac{16}{34} = \frac{8}{17} \\ \\ \Rightarrow \theta=\cos^{-1}\left( \frac{8}{17} \right) \\ \\ \\ \tan\theta= \frac{opposite}{adjacent} = \frac{30}{16} = \frac{15}{8} \\ \\ \Rightarrow \theta=\cos^{-1}\left( \frac{15}{8} \right)$

3 0

3 years ago

Your realized income is $36,864.00/yr. Your fixed and housing expenses are 32% and your savings are 15% of your realized income

andriy [413]

Answer:

You will have $1628.16 per month in discretionary money.

Step-by-step explanation:

In order to find the amount of money you have left for discretionary purposes at the end of the money, you need to calculate the total amount of your monthly pay is going towards expenses and savings. Since there are 12 months in a year, your monthly income is $3072. Of that amount, you spend 32% on housing and 15% on savings, for a total of 47%. The remaining percentage of your income would be considered discretionary, which would account for 53%. To find the amount of money, you take your monthly income and multiply it by 53%, or .53, which gives you $1628.16.

6 0

3 years ago

(1.5 ? 10^2) X (2.0 ? 10^3) Express your answer in scientific notation and standard form.

ludmilkaskok [199]

Answer: 3*10^5 or 300,000 cant remember witch one it is

Step-by-step explanation:

1.5*10^2= 150

2*10^3=2,000

150*2000=300,000

3*10^5

4 0

3 years ago

Hey everyone !

zhuklara [117]

Answer:

The measure of the largest angle is 120°

Step-by-step explanation:

Lets explain how to find the measure of an angle from the length of the

sides of the triangle

- We can do that by using the cosine rule

- If the three angles of the triangle are A , B , C, then the side opposite

to angle A is BC , the side opposite to angle B is AC and the side

opposite to angle C is AB, So to find measure of angle A use the rule

$cos(A)=\frac{(AB)^{2}+(AC)^{2}-(BC)^{2}}{2(AB)(AC)}$

Lets solve the problem

- Assume that the triangle is ABC where AB = 14 cm , BC = 10 cm and

AC = 6 cm

- We need to find the measure of the largest angle

- The largest angle is opposite to the longest side

∵ The longest side is AB

∴ The largest angle is C

By using the rule above

∴ $cos(C)=\frac{(AC)^{2}+(BC)^{2}-(AB)^{2}}{2(AC)(BC)}$

∵ AB = 14 cm , BC = 10 cm , AC = 6 cm

∴ $cos(C)=\frac{(6)^{2}+(10)^{2}-(14)^{2}}{2(6)(10)}$

∴ $cos(C)=\frac{36+100-196}{120}$

∴ $cos(C)=\frac{-60}{120}=-0.5$

∴ cos(C) = -0.5 ⇒ that means angle C is obtuse angle

∴ m∠C = $cos^{-1}(-0.5)=120$

* The measure of the largest angle is 120°

8 0

2 years ago

Read 2 more answers

Can someone please help me find the measure of angle ABO?

lara [203]

Answer:

m<ABO = 22 deg

Step-by-step explanation:

A tangent intersects a circle at the point of tangency making a right angle with the radius drawn to that point. That means that <BAO is a right angle and measures 90 deg. That makes the other two angles of the triangle complementary with a sum of 90 deg.

m<O + m<B = 90

68 + m<B = 90

m<B = 22

Answer: m<ABO = 22 deg

3 0

3 years ago