Final answer:
To find the altitude AH in ∆ABC with legs AC and BC of 17 m each and an angle at C of 40°, we can calculate using the sine function: AH = AC * sin(∠C).
Step-by-step explanation:
The question is about finding the altitude of a triangle (∆ABC). Given ∆ABC with AC=BC=17 m and ∠C=40°, the task is to find the length of the altitude AH. Using trigonometry and the properties of an isosceles triangle, we can find the length of AH.
First, we can divide ∆ABC into two right-angled triangles by drawing altitude AH. In right-angled triangle AHC:
AH = AC * sin(∠C) = 17 m * sin(40°)
After calculating this using a scientific calculator, we get the length of AH.
Knowing the length of the altitude AH can be helpful in various applications, such as finding the area of ∆ABC, understanding the geometric properties of the triangle, or solving related problems in trigonometry.