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3 years ago

Which is a true statement about a 45-45-90 triangle?

Mathematics

1 answer:

AlekseyPX3 years ago

7 0

The answer should be
D. The hypotenuse is v2 times as long as either leg.

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A firework is launched at the rate of 10 feet per second from a point on the ground 50 feet from an observer. to 2 decimal place

Kazeer [188]

The rate of change of the angle of elevation when the firework is 40 feet above the ground is 0.12 radians/second.

First we will draw a right angle triangle ΔABC, where ∠B = 90°

Lets, assume the height(AB) = h and base(BC)= x

If the angle of elevation, ∠ACB = α, then

tan(α) = $\frac{AB}{BC} = \frac{h}{x}$

Taking inverse trigonometric function, α = tan⁻¹ ( $\frac{h}{x}$ ) .............(1)

As we need to find the rate of change of the angle of elevation, so we will differentiate both sides of equation (1) with respect to time (t) :

$\frac{d\alpha}{dt}=[\frac{1}{1+ \frac{h^2}{x^2}}]*(\frac{1}{x})\frac{dh}{dt}$

Here, the firework is launched from point B at the rate of 10 feet/second and when it is 40 feet above the ground it reaches point A,

that means h = 40 feet and $\frac{dh}{dt}$ = 10 feet/second.

C is the observer's position which is 50 feet away from the point B, so x = 50 feet.

$\frac{d\alpha}{dt}= [\frac{1}{1+ \frac{40^2}{50^2}}] *\frac{1}{50} *10\\ \\ \frac{d\alpha}{dt} = [\frac{1}{1+\frac{16}{25}}] *\frac{1}{5}\\ \\ \frac{d\alpha}{dt} = [\frac{25}{41}] *\frac{1}{5}\\ \\ \frac{d\alpha}{dt}= \frac{5}{41} =0.1219512$

= 0.12 (Rounding up to two decimal places)

So, the rate of change of the angle of elevation is 0.12 radians/second.

5 0

3 years ago

8-m/n +p^2 when m=8,n=2,p=2

expeople1 [14]

8 - m/n + p^2

8 - 8/2 + 2^2

8 - 4 + 4

4 + 4

⭐ Please consider brainliest! ⭐

✉️ If any further questions, inbox me! ✉️

8 0

4 years ago

In the figure below an you can see the pic plis help

Anni [7]

The measure of angle 1 and 2 should add up to 180°, because it forms a straight line. The same goes for the sum of angle 3 and 4.

Since we are given the measure of angle 2, we can find the measure of angle 1 by subtracting 143° from 180°.

180°-143° = 37°

We know that the intersecting lines form 2 sets of vertical angles, which are congruent. This means that the angles opposite from each other have the same measure. Therefore, both angle 2 & 4 have a measure of 143°, while angle 1 & 3 have a measure of 37°.

4 0

4 years ago

Find the measure of the missing angle.

natulia [17]

Answer:

x = 76

Step-by-step explanation:

The inscribed angle x is half the measure of its intercepted arc.

x = $\frac{1}{2}$ × (102 + 50) = 0.5 × 152 = 76