what are the lengths of the two other sides of a triangle when the base is 30 ft and the base angles are 30deg

Question

this is to settle a bet - i can't think of the formula - but we know one length of a triangle = 30 ft - and the two angles on either side of the base are 30 deg each - what is the lenght of the other two sides?

Answer 1

this is too easy. Think of the triangle as two right triangles joined together. both the other sides are of equal length (since they are opposite the 30 degree angles)

Base is 30 ft

THerefore half of base is 15 (when you drop a perpendicular from tip to the base)

Call the side length x

then cos(30) = 15/x from tables this = root(3)/2

therefore x = 30 / root(3) = 17.32 feet

This is your side length

Answer 2

If the base is 30 ft and the base angles are 30 degrees, the triangle is isosceles. The altitude of the triangle divides the triangle into two congruent right triangles. We can use trigonometry to determine the length of the other two sides.

cos 30 = sqrt 3 / 2
sqrt 3 / 2 = 15 / x (15 is the length of the base of the right triangle)
x sqrt 3 = 30
x = 10 sqrt 3 = 17.32 ft

Since the triangle is isosceles, both the other sides are 17.32 ft in length.

Answer 3

Oh, ok. let me take a shot at this question. ok, so the information that we have is the length of the base which is 30ft. and each of the base angles of the triangle is 30 degrees. according to this information we can conclude that this is an isoceles triangle, according to the converse of the base angles theorom which states that " if two base angles of a triangle have equal degree measures then the legs opposite those angles are congruent( meaning equal in length)" we also have to consider the properties of an isoceles triangle. Another property states the if a perpendicular line is drawn from the vertex of the angle formed by the two congruent sides then it bisects the opposite side. so according to this information we now have two triangles each of base 15 ft because we used a property that splits it in half. and sice we just drew a perpendicular line we now have a 30-60-90 triangle. because[ 180-(90+30)=60] hence leading to our conclusion. the next thing we have to do is look at the properties of a 30-60-90 triangle. if the length of the longer leg which is 15 ( longer leg is opposite the 60 degree angle) then the length of the shorter leg( opposite the 30 degree angle) is 15/radical 3( square root of 3) then the length of the hypotenuse is (15/radical 3) x 2
which gives you 30/radical 3 so the length of each of the other two legs is 30/radical 3. another way to solve this is using the pythagorean theorm which states that a^2+b^2=c^2. we determined that the base is 15 and the height is 15/ radical 3
so you then set up an equation (15^2)+(15 /radical 3)^2= c^2
then 225 + 75 =c^2 --> which ultimatley yields 30 over radical 3. now lets look at it from trigonometry.

sin60=15/x
sin60x=15
x=15/sin60 = 30/ radical 3

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Answer 4

This is an isosceles triangle, with the third angle being 120.
This angle is between two identical sides, assume each of which as x.
So by using the cosine rule, taking 120 as the wanted angle:

c^2 = a^2 + b^2 - 2ab cos x
c is the 30 ft side, a and b are the identical ones, and x is the 120

so : 30^2 = x^2 + x^2 - 2*x*x*cos120
900 = 2x^2 -[ 2(x^2)(-1/2)
900 = 2x^2 + x^2 = 3x^2
x^2 = 300
x= 17.32 ft is the measure for each of the two sides.

Answer 5

since the base angles are equal,the other sides of the angle are equal too,so the answer is 7.5ft for each
the formula:
180-(30+30)=120
this is the othe angle.
x/30=30/120
x=7.5

Answer 6

nearly 17.5 feet each ...i guess...i hope it is correct... and i would like to also say that trigonometry cannot be used in this..since there's no 90 degrees in the triangle.

Answer 7

tan30 deg=opp/adj
adj =30ft
theerfore opp= adj*tan 30 deg=ans
cos30=adj/hyp
therefore hyp=adj/cos30 deg= ans