Question

two sides being given, calculate the third side marked by a letter in each right angled triangle.​

Answer 1

Answer:

20

Step-by-step explanation:

By Pythagoras theorem,

${d}^{2} = {29}^{2} - {21}^{2} \\ {d}^{2} = 841 - 441 \\ {d}^{2} = 400 \\ d = \sqrt{400} \\ d = 20$

Answer 2

Answer:

base length (d) = 20 units

Step-by-step explanation:

Given Triangle is a Right Triangle,

So, using the Pythagoras theorem, we have

$a^{2} + b^{2} = h^{2}$

where, a = altitude

b = base = d

h = hypotenuse

Hypotenuse and altitude is given, 29 units and 21 units respectively,

Since

$a^{2} + b^{2} = h^{2} \\ b^{2} = {h}^{2} - {a}^{2} \\ b = \sqrt{ {h}^{2} - a^{2} } \\ b = \sqrt{29^{2} - 21^{2} } \\ b = \sqrt{841 - 441}$

$b = \sqrt{400} = 20$

Hence, base length (d) = 20 units