The lengths of a triangle are consecutive odd numbers The perimeter is 87 cm what is the length of the longest side
2 answers:
You might be interested in
Answer:
x ≈ 37.53
Step-by-step explanation:
To find the value of x, we will follow the steps below:
first, we need to find angle z
z+47° +90° = 180° (sum of interior angle of a triangle)
z + 137° = 180°
subtract 137° from both-side of the equation
Z + 137°-137° = 180° - 137°
Z=43°
angle Z = 43°
We can now use the sine rule to find the value of x
Using the sine rule
where Z and X are angles and z and x are side length
from the diagram given,
X = 47° and we find Z to be 43°
side z = 35
we can now proceed to substitute the values into the formula
=
cross-multiply
x sin 43° = 35 sin 47°
divide both-side of the equation by sin 43°
x sin 43° /sin 43°= 35 sin 47° /sin 43°
x ≈ 37.53 to two decimal place
With the markings on the triangle, we know that this is an isosceles triangle. This makes m∠B=m∠C.
Let x=m∠B. We know that all the angles in a triangle must add up to 180°
m∠A + m∠B + m∠C = 180
We know that m∠A=118°, m∠B=x, and m∠C=m∠B=x. Using this information, the equation changes to:
Subtract both sides by 180
Divide both sides by 2
Since x=31, m∠B must be 31°.
This explanation might be a bit confusing, so let me know if you need any clarifications, thanks!
~ Padoru