The large triangle is an isosceles since both angles at the base each equal 42°.
In an isosceles triangle the altitude z is at the same time median , then it bisects the opposite side in the middle . So w = 120/2 = 60

Now let's calculate z:
tan 42° = (opposite side) / (adjacent side) = z/60
tan 42° = 0.9,
0.9 = z/60 and z = 54

6 0

3 years ago

Find 2 numbers a and b such that (a-b)^2 < (a+b)(a-b)< (a+b)^2 Find two numbes a and b such that this is not true

Svet_ta [14]

Suppose for the moment that the inequality holds for all $a,b$ :

$(a-b)^2$

Expanding everything gives

$a^2-2ab+b^2$

$\implies-ab$

In particular, the inequality says that $-ab$ for any choice of $a,b$ . But if $a$ and $b>0$ , then $-ab>0$ while $ab$ .

So one possible choice of $a,b$ could be $a=-1$ and $b=1$ . Then we get

$(-1-1)^2=4$

$(-1+1)(-1-1)=2$

$(-1+1)^2=0$

but clearly it's not true that $4$ .

8 0

3 years ago

What triangle pairs can be mapped to each other using a single tranlation

shepuryov [24]

Answer: I think Figure 4 is the correct one

Step-by-step explanation:

It is not possible to map the triangle MNP and CDE together using just a single translation in Figure 3. With Figure 4, we can use a translation to map the triangle MNP and the triangle CDE. Accordingly, in the diagram, the triangle MNP and the triangle CDE can be translated to each other.

8 0

3 years ago