Given qr = 4.8, m angle r space equals space 80 degree , and m angle p equals 42 degree ... if you want to find pq.... a. should
1 answer:
By applying the law of sines, the length of side PQ is equal to 7.1 units.
<h3>What is the law of sines?</h3>The law of sines is also referred to as sine law and it can be defined as an equation that relates the side lengths of a triangle to the sines of its angles.
<h3>How to calculate the length of PQ?</h3>Mathematically, the law of sines is given by this equation:
Substituting the given parameters into the formula, we have;
PQ = 7.1 units.
Read more on law of sines here: brainly.com/question/7922954
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Answer:
UV=29
Step-by-step explanation:
In right triangles AQB and AVB,
∠AQB = ∠AVB ...(i) {Right angles}
∠QBA = ∠VBA ...(ii) {Given that they are equal}
We know that sum of all three angles in a triangle is equal to 180 degree. So wee can write sum equation for each triangle
∠AQB+∠QBA+∠BAQ=180 ...(iii)
∠AVB+∠VBA+∠BAV=180 ...(iv)
using (iii) and (iv)
∠AQB+∠QBA+∠BAQ=∠AVB+∠VBA+∠BAV
∠AVB+∠VBA+∠BAQ=∠AVB+∠VBA+∠BAV (using (i) and (ii))
∠BAQ=∠BAV...(v)
Now consider triangles AQB and AVB;
∠BAQ=∠BAV {from (v)}
∠QBA = ∠VBA {from (ii)}
AB=AB {common side}
So using ASA, triangles AQB and AVB are congruent.
We know that corresponding sides of congruent triangles are equal.
Hence
AQ=AV
5x+9=7x+1
9-1=7x-5x
8=2x
divide both sides by 2
4=x
Now plug value of x=4 into UV=7x+1
UV=7*4+1=28+1=29
<u>Hence UV=29 is final answer.</u>
we know that
The area of the hexagon is equal to the sum of the areas of the six equilateral triangles
Let
x-------> area of one equilateral triangle
so
Divide by both sides
-------> area of one equilateral triangle
To find an equivalent expression for the area of the hexagon based on the area of a triangle, multiply the area of one equilateral triangle by
therefore
the answer is
The equivalent expression is equal to