The technis OSTS SSL BUS 57.98

Given:

diamong [38]

Answer:

10-5 $\sqrt{2}$

Step-by-step explanation:

As per the attached figure, right angled $\triangle MDL$ has an inscribed circle whose center is $I$ .

We have joined the incenter $I$ to the vertices of the $\triangle MDL$ .

Sides MD and DL are equal because we are given that $\angle M = \angle L = 45 ^\circ.$

Formula for area of a $\triangle = \dfrac{1}{2} \times base \times height$

As per the figure attached, we are given that side a = 10.

Using pythagoras theorem, we can easily calculate that side ML = 10 $\sqrt{2}$

Points P,Q and R are at $90 ^\circ$ on the sides ML, MD and DL respectively so IQ, IR and IP are heights of $\triangle$ MIL, $\triangle$ MID and $\triangle$ DIL.

Also,

$\text {Area of } \triangle MDL = \text {Area of } \triangle MIL +\text {Area of } \triangle MID+ \text {Area of } \triangle DIL$

$\dfrac{1}{2} \times 10 \times 10 = \dfrac{1}{2} \times r \times 10 + \dfrac{1}{2} \times r \times 10 + \dfrac{1}{2} \times r \times 10\sqrt2\\\Rightarrow r = \dfrac {10}{2+\sqrt2} \\\Rightarrow r = \dfrac{5\sqrt2}{\sqrt2+1}\\\text{Multiplying and divinding by }(\sqrt2 +1)\\\Rightarrow r = 10-5\sqrt2$

So, radius of circle = $10-5\sqrt2$

8 0

2 years ago

Donald’s salary last year was $65,000. The tax system says •any income under $20,000 is tax free. •Any income between $20,000 an

likoan [24]

Answer:

hey can you help me with this? it's my deadline today

8 0

2 years ago

Sally was standing 30 feet from a tree. The angle of

QveST [7]

Answer: The tree was 27 feet tall

Step-by-step Explanation: First of all Sally was standing 30 feet away from the tree and she looks up at an angle of elevation of 38 degrees to the top of the tree. With this bit of information we can determine that a right angled triangle has been formed with the reference angle as 38 degrees, the side facing it as h (the height of the tree) and the adjacent side as 30. We shall apply the trigonometric ratio as follows;

Tan 38 = opposite/adjacent

Tan 38 = h/30

0.7813 = h/30

0.7813 x 30 = h

23.4 = h

We remember at this point that Sally’s eyes were 4 feet above the ground. What we have just calculated is the height of the tree from “4 feet above the ground” (where her eyes were). Hence the actual height of the tree is calculated as 23.4 plus 4 which gives us 27.4

Therefore the tree was 27 feet tall (approximately to the nearest foot)

5 0

3 years ago

Can someone help me with factoring by grouping please show step by step

ValentinkaMS [17]

Answer is 3-110x

3 times 1 squared - 11 times 10
1 raised to any power equals 1

calculate the product
3 times 1 -110x

any expression multiplied by one stays the same
3-110x

i hope this helped! thanks!

4 0

3 years ago

Two large single-topping pizzas cost $25.00. What is the constant of proportionality

Brrunno [24]

i do not know kid -_-

4 0

3 years ago

The technisOSTSSSL BUS 57.98​

The technisOSTSSSL BUS 57.98