The diagram shows a semi circle inside a rectangle of length 140m. the semi circle touches the rectangle at P, Q and R. Calculat
e the perimeter of the shaded region. give your answer correct to 3 significant figures. ITS ON MATHSWATCH PLS HELP!!!
1 answer:
Answer: 250m
Step-by-step explanation:
Length of rectangle = 140m
Length of rectangle = diameter of semicircle = 140m
Therefore, Radius(r) = 140m / 2 = 70m
Perimeter of the shaded region:
Length of tangent at P + length of tangent at Q + shaded portion of arc(AB)
Length of tangent = diameter / 2
Length of tangent = 70m
Perimeter of a circle = 2πr = 2 × 22/7 × 70 = 440m
shaded portion = 440 / 4 = 110m
Therefore, perimeter of shaded portion equals
70m + 70m + 110m = 250m
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Hi there!
<u>What we need to know:</u>
The three main trigonometric ratios are sine, cosine and tangent:
"Opposite" refers to the side opposite the angle that is not the hypotenuse.
"Hypotenuse" refers to the side opposite the right angle of a right triangle.
"Adjacent" refers to the side next to the angle that is not the hypotenuse.
"θ" is read as "theta". It just represents the angle.
Keep in mind that these three ratios only apply to right triangles.
You can use the mnemonic "soh-cah-toa" to help you remember these ratios.
<u>First question</u>
For the first question, we're given the angle with a measure of 56 degrees and the length of the <em>hypotenuse</em>. We must calculate <em>a</em>, which represents the side <em>adjacent </em>to the given angle.
Given the hypotenuse and the adjacent side, we know that we must use the cosine ratio:
Plug in the given information:
Isolate <em>a</em> by multiplying both sides by 13:
Solve using a calculator:
Therefore, <em>a</em> is equal to 7.3 when rounded to 1 decimal place.
<u>Other information you will need to know:</u>
In the above question, we needed to solve for a side. But what if we were given two sides and we needed to solve for an angle? For example:
In this case, we will use the inverse sine ratio:
Solve using a calculator:
Therefore, the angle would equal approximately 39 degrees.
I hope this helps!