How do you know to use trig ratios

In the figure below, AB=AC=50, AD=52, and BC=28. Determine CD.

Tanzania [10]

Check the picture below, on the left side.

since the triangle ABC is an isosceles with twin sides, if we drop a line bisecting the angle at the vertex A, we end up with a perpendicular line that cuts the "base" in two equal halves, so then

$\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{50}\\ a=\stackrel{adjacent}{14}\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{50^2 - 14^2}\implies \sqrt{2500 - 196}=b\implies \sqrt{2304}=b\implies 48=b$

as you can see in the picture in red, now let's find CD.

$\stackrel{\textit{pythagorean theorem}}{\sqrt{52^2 - 48^2}=14}+CD\implies \sqrt{2704-2304}=14+CD \\\\\\ \sqrt{400}=14+CD \implies 20=14+CD\implies 6=CD$

8 0

2 years ago

The radius of the base of a cylinder is decreasing at a rate of 121212 kilometers per second. The height of the cylinder is fixe

WARRIOR [948]

Answer:

7536 $km^3/sec$

Step-by-step explanation:

Given that:

Rate of decreasing of radius = 12 km/sec

Height of cylinder is fixed at = 2.5 km

Radius of cylinder = 40 km

To find:

The rate of change of Volume of the cylinder?

Solution:

First of all, let us have a look at the formula for volume of a cylinder.

$Volume = \pi r^2h$

Where $r$ is the radius and

$h$ is the height of cylinder.

As per question statement:

$r$ = 40 km (variable)

$h$ = 2.5 (constant)

$\dfrac{dV}{dt} = \dfrac{d}{dt}\pi r^2h$

As $\pi, h$ are constant:

$\dfrac{dV}{dt} = \pi h\dfrac{d}{dt} r^2\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2 r\dfrac{dr}{dt} \\$Putting the values:$\\\Rigghtarrow\dfrac{dV}{dt} = 3.14 \times 2.5\times 2 \times 40\times 12 \\\Rigghtarrow\dfrac{dV}{dt} = 7536\ km^3/sec$

4 0

3 years ago

Please answer this question now

Tema [17]

Answer:

Surface Area = 85.75 ft²

Step-by-step explanation:

Surface area of pyramid = ½(Perimeter of triangular base * slant height of pyramid) + Area of triangular base

Perimeter of triangular base = sum of all sides of the triangular base = 5+5+5 = 15 ft

Slant height of pyramid = 10 ft

Area of triangular base = ½*base of triangle*height of triangle = ½*5*4.3 = 10.75 ft²

Plug in the above values:

Surface Area = ½(15*10) + 10.75

= (15*5) + 10.75

= 75 + 10.75

Surface Area = 85.75 ft²

8 0

4 years ago

If a translation maps 2D onto 2B, which of the following statements is true?

Wewaii [24]

Answer:

The last one is the answer CD=CB

6 0

2 years ago

What's 2+2? Please explain how you got this answer.

Neko [114]

Answer:

2+2=4

Step-by-step explanation:

1+1+1+1=4

4 0

3 years ago