A base angle of an isosceles triangle measures 45 degrees and the length of one of the legs is 12. What is the length of the altitude drawn to the base of the triangle?

The length of the altitude drawn to the base of the triangle is 8.49

Step-by-step explanation:

In this question, we are asked to calculate the length of the altitude to the base of an isosceles triangle given the length of one of the legs and the base angle. To answer this sufficiently, we consider the diagram of the triangle in the attached file.

From the triangle , we can see that we want to calculate the length h.

Let’s look at a cut-out triangle from the big triangle. This is the triangle AOC

WE can calculate the length of h here, using trigonometric identity. What we have is the hypotenuse and the opposite, this means that the trigonometric identity to use is the sine

Sine 45 = h/12

h = 12 * sine 45

Sine 45 = 0.7071

h = 12 * 0.7071

h = 8.49

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.