hình,
~~~
a/ \(\widehat{MNP}=90^o-\widehat{P}=90^o-53^o=37^o\)
Ta có: \(sinP=\dfrac{MN}{NP}\)
=> \(MN=sinP\cdot NP\approx11,98\left(cm\right)\)
\(cosP=\dfrac{MP}{NP}\Rightarrow MP=cosP\cdot NP\approx9,03\left(cm\right)\)
A/dụng hệ thức lượng trong tam giác MNP vuông tại M có:
+) MN2 = NP . NH
=> NH = \(\dfrac{MN^2}{NP}=\dfrac{11,98^2}{15}\approx9,57\left(cm\right)\)
+) MH2 = NH . PH = NH . (NP - NH) = 9,57 . (15 - 9,57) = 51,9651
=> MH = 7,21 (cm)
b/ Vì ND là p/g góc MNP
=> \(\dfrac{MD}{MN}=\dfrac{DP}{NP}=\dfrac{MD+DP}{MN+NP}=\dfrac{MP}{11,98+15}=\dfrac{903}{2698}\)
=> DP = \(\dfrac{903}{2698}\cdot NP=\dfrac{903}{2698}\cdot15\approx5,02\left(cm\right)\)
vậy...
