The height to the base of an isosceles triangle is 12.4m, and its base is 40.6m. what are the measurement of the angles of the triangle and the length of its legs?

Base Angles=31.42°

Length of legs=23.79 m

Vertex angle=117.16°

Step-by-step explanation:

An isosceles triangle is a triangle whose leg lengths are equal. They also form base angles that are equal.

Base angles can be solved by using the tan of one of the base angles, let the base angle be ∅.

Using the formula Tan∅=opposite/adjacent

Where the opposite side=Height=12.4 m, and the adjacent side=0.5×Base length= 0.5×40.6=20.3 m

Tan∅=12.4/20.3=0.61

∅=(Tan∧-1)×0.61=31.42°

Base angle=31.42°

  2. Length of legs

The length of each of the legs can be g the formula

Hypotenuse=√((Height)²+(0.5×base length)²)=√(12.4²+20.3²)=23.79 m

Length of the legs=23.79 m

3. Vertex angle

Let the vertex angle be x

Total angles in a triangle should add up to 180°, meaning

(2×base angle)+vertex angle=180°

(2×31.42°)+x=180°

62.84+x=180

x=180-62.84=117.16°

Vertex angle=117.16°

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step-by-step explanation:

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.